Maybe the problem is in the interpretation of the right of free speech.
It means that the government, or anyone for that matter, CANNOT pass any laws or what have you restricting your right to speak freely. But free speech doesn't mean "no consequences." There are still places where it's simply not appropriate to do or say certain things. (I'm not relating your your situation, specifically, Mental, I'm just speaking generally)
Like, there's no law that says "you can't say the f word in a public school." That would be a violation of free speech. However, if you DO say the f-word in a public school, you'll be punished because it's not appropriate to say that in a public school. Not because you're not allowed to say it, PERIOD, or because some law prohibits you from saying it. No, because public school's are filled with young, impressionable children, and the f-word is NOT appropriate there!
.....eh......that still doesn't prove anything either way, I guess. It certainly is a troublesome little right...