Given the information provided I'd say it's highly likely his mobile device was the attack surface used. I don't use Coinbase, but a glance at their API docs makes it appear that the API key alone isn't sufficient to initiate a transfer since authentication is required.
If that's the case, this is analagous demanding a refund from your bank when your account was emptied because you lost your wallet, ATM card and a postit note with the PIN # written on it.
nbs