This pretty much nails it - the insane often do let their fantasies rule them, and what that fantasy is is often a matter of fashion, as what they fixate on can be random.
In the 19th century it seems that it was a fashion among the insane to imagine themselves as Napoleon, or Napoleon-like.
Now they get the idea they are the other sex.
Telling a man that believes that he is a woman that it is so is akin to giving a man that believes that he’s Napoleon a funny hat and a sword and telling him that if he invades Russia he’ll feel better about himself.