A person can be severely mentally ill in many ways, not all of them are highly public and immediately offensive to passers by. So while the people you describe would indeed fall into that category, many readers would likely place other people with debilitating mental illnesses into that category as well.
That's true, but someone who is severely mentally ill in an invisible way is not going to be categorized as such by a passerby, so it's an obviously semantic ambiguity. Saying what is technically true but not understood is just distracting.
That's not necessarily true either. Someone who is catatonic might be noticed by a passerby but doesn't scream "this person isn't safe to have in a shelter".
