While I see where you are coming from, that's your definition of "burnt out", but it is not the only valid one, and many obviously don't require the condition to be as extreme as you do for the term to be valid.

I don't know anything about Jason, so I can't make an informed call on whether I think he is overly exaggerating things by using the term.

I do think there is at least a version of "burnt out" that just means you are really tired, because you have put a lot of effort into something for a long period of time, to the point that you are questioning whether it is worth it to you to continue doing it.

However, yeah, some people probably say "I'm so burnt out on 'X'" because they've spent over a half hour on it, and it still isn't done. That doesn't qualify, in my opinion.