Someone "naked on the street, screaming at a wall, eating a pigeon or whatever" could be having a bad trip on some drugs, not necessarily mentally ill. The drugs will wear off, and they will be a regular neurotypical person again. But by slapping a mental illness label onto that person, you've proven that you have no clue what you're talking about, and you shouldn't be diagnosing anyone.

Our brain is designed through evolution to slap labels, aka engage in hasty generalisation. The world is much more complex than that.