therearetwogenders

Yes, it's false hope for both the kid and the parents, who understandably find it a lot harder to accept the idea the cause of the person's struggles cannot be treated in any way. A very cruel false hope that leads to unnecessary medical procedures and confusion at why the person still doesn't have friends or feel like socializing comes naturally. I wouldn't be surprised if this sense of confusion is a source of a lot of the aggressiveness people who are trans demonstrate towards people they feel aren't validating them - they may genuinely not understand that not every problem they have with socializing comes from "transphobia". Naturally they will trust the so-called experts when they say so, and unlike someone who has better instincts for reading people, they may genuinely be in the dark about why people react to them the way they do. And of course, when a bunch of doctors and otherwise educated, respected people tell them it's actually society that is the problem, they will believe it. Even a normal person would.

There's a case to be made about people ASD feeling a sort of body alienation or body dysphoria as well, that might be mistakenly assumed to come from their gender - one of the symptoms is problems with coordinating movements, and also facial expressions. The "body language" and voice passing practice trans people tend to do may actually help with that by improving their motor skills, training them to be more aware of their body and gaining better control over their voice, further cementing the belief that the issue is with their gender.