Earlier quoted context omitted.
Asking for money you're owed never makes you a "douche". It doesn't take stones to ask for what you're owed just because you caused some problems. There is no link between the two! I'm astonished that anyone thinks there is. There's absolutely no leeway to say, "I don't like what you did recently, therefore I'm not going to pay you the money you're owed for something completely unrelated."
There sure is leeway: no signed contract. If he had left on good terms they would have paid the bonus, no question. He didn't and his fuckup cost them a lot more than $10k. At this point, dig in their heels. He says an email is a contract? OK, well, two can play that game. I'd bet that on the bottom of several of those emails there was something about "this email is only addressed to the sender, it may not be reposte…
Non-disclosure text at the bottom of an email seems like a real stretch for that. Of course it depends on the jurisdiction and the case law.