I don't think he has no choice but to return it just like what you have said they know his address and name. But I think it's the exchange's fault and not the user the good thing to do is to maybe give the user a reward for returning the Bitcoin but if the buyer becomes greedy well I'm not sure what will be the PDAX's move after that.
I do not think it is as clear cut as you make it out to be, if this was the result of some bug then that may be the end result especially if that is specified within the TOS of that exchange, however if this was a mistake on their end and the user legitimately bought those coins and simply took advantage of the cheap price that was shown then this is going to be way more difficult for the exchange to prove they have a right on those coins.
Also it will depend on the amount of money we are talking about, for an exchange to do this I suppose the amount is large in which case the user could hire legal representation if he really believes those coins belong to him.