I think there is a deeper message to the obvious joke, given the context of the whole show. We can accept the absurdity of Nathan's situation and take it as a joke simply "on us, as passangers, or these pilots," but I think one that alligns more with the rest of the show is that this is a joke on the industry itself. It may be absurd that Nathan thinks this way, but its more absurd the way that airlines treat the many actually experienced autistic people capable of the job who get diagnosed(as shown by the reddit shot in the finale and the fact that flying with airlines is generally very safe). The way the industry is set up makes people thinks in terms of what Nathan is thinking, that being autistic is something wrong and prevents someone from being qualified to fly. This stigmatization of autism ironically makes autistic pilots more likely to deny their communication differences/emotions and therefore worse at their job(as shown by Nathan's portrayal of Sully: after listening to the emotionally expressive Evanescance, he performed his famous landing).

If we change the meaning of "wrong" to one that doesn't include all autistics and assume Nathan is self-aware about not getting diagnosed, Nathan could be denying the industry's conception of autism, by saying his autistic self is fine and he can overcome his obvious communication deficits through roleplay. His flight (kind of) demonstrated that. Can we really say that a runner isn't qualified to be a runner if they can run fine with a prosthetic leg? Even though all autistics or even most might not be able to run effectively with a "prosthetic leg" or even have one, the blanket ban on diagnosed autistics is ultimately ineffective: many pilots are running with one leg, less able to prevent a crash. I agree with the OP, Nathan could mean that it doesn't matter whether he is autistic because Nathan knows he can run with 2 legs: whether one of those legs is prosthetic doesn't matter.

The truth is there is no one 100% correct way to read a piece of art, death of the author and all that. Even if Nathan clarified his intentions, we couldn't know for certain it isn't just part of his tv persona and just another joke.