That looks like it's easy to work around:

1. Deposit from one address (your wallet) and verify ownership by sign message or something - do they even allow that?
2. Now you can withdraw money from any exchange, mixer, website, or dark money service, send all the withdrawals to another address, transfer the entire balance of said address or part of it to the verified address and then deposit.
3. Bitstamp won't say anything (but it remains to be seen if they are that gullible. My sources say no.)