Box & DA,
If you're asking "Where in the Bible does it say that the use of 12-gauge rubber buckshot is considered deadly force?", I'm not going to do your research for you.
You are fully capable of following up in your own jurisdiction, wherever it is, with your local state laws and your local prosecutorial office.
It's incorporated into case law, PD use-of-force policies, and state laws from coast to coast. The original label "less than lethal", as you noticed, is generally no longer used, it's now referred to correctly as "less lethal", including the company you linked to, which should tell you something.
Less lethal ammunition has caused serious injury, and no- I'm not going to look it up for you. Do your own homework.
Legally, the yardstick is some form of verbiage that includes words such as likely to, or known to, cause death or serious/grievous bodily injury, and these rubber shotshells are capable of doing that. As such, they fall under the same statutes governing the use of any deadly force encounter. Most of those include a foundation of impending threat to persons, not property.
That's for a criminal prosecution against the user deemed to have exceeded the required parameters for its use. A civil action requires much less to prevail.
"...if used in the prescribed manner...", which means by those trained in its use, following use protocols, and acting in certain situations where it genuinely is a viable alternative, again a different ballgame.
Where police have a requirement to terminate an encounter in many situations to resolve those situations, you do not.
Where police may need to subdue & control a resistive subject for any one of a number of reasons, you do not.
Where police cannot walk away from a man who may be out of control but not offering them a direct threat to them, you can.
Where police have to subdue and the force necessary to do so doesn't justify deadly force, but there is a risk of police injury in merely the laying on of hands, less lethal means are perfectly acceptable, WHEN USED IN ACCORDANCE WITH MANUFACTURER'S RECOMMENDATIONS, DEPARTMENT TRAINING & POLICIES, AND IN CERTAIN NARROWLY PRESCRIBED WAYS.
Generally, where possible, that means using a specific type of less lethal ammunition with multiple officers present & able to step in and handcuff when the subject goes down, and to immediately radio for medical response. (Exigent circumstances are allowed for.)
Such ammunition is used in tightly controlled circumstances, and the wise department that issues the stuff also makes damn sure it's carried in a dedicated less-lethal-ONLY shotgun, to avoid a mixup in who's got what in what shotgun, and the subject getting seriously shot by the real thing.
Officers don't just get handed a handfull of LL loads & told to "Go use it wherever you feel like using it."
You can rest assured each use of LL is closely scrutinised by any department with half a brain & even a moderately competent city or county attorney who doesn't want to lose huge chunks of money on lawsuits.
Law enforcement has a totally different set of rules of engagement than you do.
They are allowed to use LL ammo as a recognized function of their mandate to subdue, as a permissable level of their continuum of force in doing so.
You are not.
In their continuum, they are allowed a wider lattitude in disparity of force than you are because they are also allowed to engage aggressively in a very wide range of circumstances that you simply aren't.
In your hands, LL is considered deadly force, in theirs it's not.
Double standard? Yes, but but totally different rules. They can be aggressive, you're pretty much required to be defensive.
The average "civilian" gets no training, does not know the legal pitfalls, does not know how to properly use the stuff, doesn't understand it, and is infinitely more likely to either misuse it or mix it up with regular loads in the same gun.
Repelling the threat?
In most homes, distances are close. If you're familiar with the Tueller Drill you know that a determined body can be all over you with knife or club in an average time of 1.5 seconds, from an initial starting distance of 7 yards, 21 feet. That's a fair distance for most houses, you're frequently much closer.
In that distance & time frame, if you determine an intruder is a genuine threat (advancing or exhibiting threatening behaviour, etc.), you will have to deal with reaction times. He may already be close, he may be moving rapidly, and you may not have time to get more than one shot off before he's standing on your chest. You want to waste that one shot in the hope that it either disabled or scared him off? I don't. You think you'll have time to fire a load of rubber, wait to see if it did what you hoped it did, and then follow up with lead?
When I was a firearms instructor for my last PD, I used to get into a regular disagreement with the instructor who conducted our baton & hands-on training. His thrust, so to speak, with a background in those two areas, was to strike & assess. That meant strike once, stop briefly to assess, and then follow up if necessary with another strike. He wanted us to incorporate that philosophy in our firearms training, and he always got told NO!
Our firearms training was then & should be now that you fire as soon as the threat is determined to be a life-threatening one, and you fire until that threat goes down. Regular live ammunition is unpredictable enough from person to person to show us we can't have the luxury of shooting once, then stopping to see if that shot changed the other guy's mind, and then firing again if it didn't.
One shot may cause the other guy to drop his gun, it may not even be noticed by him as that gun comes on target in the center of your chest.
Odds run even farther against you with rubber.
The POTENTIAL is there, the PREDICTABILITY is not.
LL ammo is unpredictable enough that I won't risk wasting my first shot on rubber if a threat inside my home is sufficiently so to justify firing at all.
You've taken time you may not have, and if your shotgun happens to carry five rounds, you may very probably have just wasted 20% of it.
I don't consider it a matter of reducing options, like I said- if a threat needs to be engaged, it needs to be engaged just as hard and just as effectively and just as SOON as I can. Such encounters can be very quick, and very close. I don't want to waste time deciding where the load has to go (legs vs torso), or firing two shots to get the benefit of one.
Less lethal in terms of deadly force is half the issue, as addressed. Effectiveness in terms of user survivability is the other half.
You seem to think you'll have loads of time to decide which type of ammunition to use. You almost certainly won't.
In such scenarios, I can tell you beyond a shadow of the slightest doubt- simplest is bestest.

You can't count on having time to waste a rubber charge that may or may not work, or to decide on whether to use it instead of a lead charge, or vice versa.
Yes, we do prefer not to take a life unless it's absolutely required, and nothing I say here comes from a desire to kill. But, you increase the chances of losing your own life in making things unrealistically complicated & handicapping yourself with ammunition not designed for the purpose of self-defense.
Back to your martial arts analogy, which doesn't fit.
You are a thinking, reasoning, reactive organism. A charge of rubber buck isn't.
You have training in applying a variable degree of hands on force, the rubber buck doesn't.
You are capable of adjusting (if you're any good

) nearly instantly to a change in position or direction or attitude of your opponent, a rubber buck charge isn't.
You can single out an individual arm or leg as appropriate & apply a measured degree of force your training has hopefully taught you will be effective in obtaining the result you want, rubber buck can't.
LL loads go where the muzzle's pointing, with the same degree of force each time. They are non-reactive. They can't be recalled or re-directed in flight like your arms, hands, and legs can.
YOU can decide just before the strike lands or the action engages whether or not it'll be lethal, the rubber just strikes & does its thing.
"Mr. Armstrong, did you launch a strike with your hand that COULD kill?"
"Yes, I did."
"Did it kill?"
"No sir, it did not."
"And why not?"
"Because I chose to use a degree of force with my hand that was not lethal."
"And how did you know it would not be lethal?"
"Because I've trained on other live bodies and observed the results, and I had sufficient time, skill, and proximity to make that instant judgement."
VS
"Mr. Armstrong, did you launch a charge of 12-gauge rubber buckshot that is known to this state to be capable of causing death or grievous bodily harm?"
"Yes, I did."
"Did it kill?"
"Yes sir, it did. BUT- I didn't MEAN to kill!"
"Were you justified in using deadly force?"
"I don't know, sir, but I didn't MEAN to KILL!"
"Were you previously aware that the use of such ammunition COULD kill?"
"Yes sir, but I didn't MEAN to kill!"
"Was the deceased a direct threat to you at the time you fired?"
"No sir, he was trying to escape through the window with my plasma TV."
"What was your purpose in shooting him?"
"To stop him from taking my TV!"
"Your Honor, the prosecution rests."
And we could go on with other similar scenarios, but that's enough for the moment.
As far as just talking about rubber buck goes, most people considering less lethal usually go for rubber buck loads because they think it'll make precise aiming less important. Beanbags are also a matter of proper training & use for police, do require more precise training, and can break a rib or stop a heart if they strike the right (or wrong) spot.
Yes, there are other types of LL loads, none of which are good choices for home defense.
Denis