In the actual stories I think the kind of insanity varies. Sometimes it's like what you describe: the character is saying/doing stuff that seems insane to others, but is actually the truth. Sometimes it's that combined with a nervous breakdown or extreme PTSD sort of thing, where their experiences break them emotionally so hard that they can't function. And the former all by itself could itself cause the latter, if the truth were incompatible enough with one's emotional needs/priorities.
So you get a guy with extreme emotional instability, combined with saying/doing things that seem delusional (but aren't). It'd be easy to see how those things in combo might look like some kind of psychosis or schizophrenia from the outside. Especially the further back you go in time. I mean, even in the modern day psychology as a science is still in it's infancy, and the state of it in the early 20th was in many ways equal parts Monty Python and Wes Craven.
Terry Pratchett had a concept something like this. "Knurd": a state of hyper-awareness on the opposite side of sobriety from drunkenness. Most people who experience it have breakdowns and are haunted by it for life. This being Discworld, there are a few major characters who have some degree of it naturally as a sort of superpower.