There's no way to definitively know. There are some things they can do to demonstrate they are, in fact, the same people, but proof is elusive. For example, they have known BTC and ETH addresses. They could sign messages from such addresses, indicating whether a relaunched domain were legit or not.
That wouldn't solve the honeypot question (if Vinnik really was an owner and gave the FBI the keys, for instance). But it would make it unlikely that some random scammers were running the ICO, particularly if it coincided with the relaunch of a re-branded site that made partial repayments.