Aidey, while I personally agree with your position, I'm afraid that the law is not yet so forward thinking. Indeed, accusing someone who doesn't have a mental illness of having one is considered to be so obviously harmful that in some states it falls into the category of defamation per se, which means the plaintiff doesn't have to prove specific damage to his reputation. It's the same as if I said someone had an STD (a category that we loved in law school, because the case law discusses "imputing a loathesome disease") when they didn't.
Incidentally, falsely saying that someone is homosexual is also, at least in some states, considered to be defamatory per se, though that's being questioned now in some places. In some states, it is still defamatory per se to "impute unchastity to a woman." Until public norms change so that these things are not considered harmful to the reputation of someone who is not mentally ill, homosexual, or unchaste, the law will likely continue to recompense harm for false or reckless statements.