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.
Why should he give BTC back just because they know his address and a name?
When you look at their TOS, I don't see on what ground they demand the BTC back
You understand and agree that PDAX operates as an exchange that facilitates buying and selling of Digital Assets.
You may use your Account to place orders to buy and/or sell Digital Assets by placing your orders through the platform.
All orders that are filed, executed, matched, or completed shall be recorded on the exchange ledger immediately.
Orders, once executed, are final and irreversible.
So, if orders are indeed irreversible once executed and if PDAX is just an exchange between the two users, how come they ask money back? Unless it's them that are selling/buying BTC. Then again, he didn't share what exactly PDAX told him is the reason for wanting the BTC back so there might be more behind the story.