I agree that a conviction is a stretch. However, I think we are debating two separate angles of this thing.
While I can see both sides of the legal interpretations of the law, I am trying to point out that, while you may win the fight in the end (by not showing your permit), is the cost and hassle really worth it? Would it be better to just show your permit to the LEO, even if you technically don't have to? Better safe than sorry?
That is something that has no uniform right/wrong answer. That can only be determined by each individual. Personally, I don't see an issue with showing the permit, and have never had a problem or second glance on the few times I have.