Sorry to intrude on your link guys, but I was a Corpsman way back in the late 70's and 80's. Naturally, I can't speak for what's going on now. I'm sure you guys went to Geneva Convention classes; we did. They explained to us that if a Corpsman carried a rifle, it automatically removed him from a higher prisoner exchange category should he get captured. (They issued us special grey ID cards with red crosses on them as I remember.) Carrying a rifle could also get in the way of completing our mission, both physically and psychologically.
Prior to getting stationed with Marine units, we had to go to a 10 week course at Pendleton called Field Medical Service School. (Ironically, we carried M16's during the course.) They went into more detail concerning the separation of duties between Corpsmen and Marines. In a nut shell, Marines, are riflemen, one and all, no matter what their MOS, Right? Corpsmen are not, otherwise the Marine Corps would train their own men as corpsmen. The primary focus of the corpsman is to maintain/return as many riflemen to action as possible. It's kind of hard to do that if your focused on dumping lead downrange. We have a different job description.
Does that mean a corpsman shouldn't know how to handle a rifle? Definitely not. What do I think Corpsmen should carry? If properly trained (we weren't), MP5-K's on a thigh rig. I remember a conversation with a Nam vet I worked for. He said, "If it comes to a point where a Corpsman really needs a rifle, one will be readily available." (He did suggest carrying ammo just in case.)
Marine's used to have a saying,"What is the Marine's biggest hazard in the battlefield?" A CORPSMAN WITH A 45.