In all fairness, this isn't much different from commodity ETFs promising that they have a warehouse of gold or silver somewhere that matches the market cap of the fund. There's no easy way to completely, 100% verify this, so people just trust them.
They may not be. $30 mil is a small percentage though. Bitfinex makes a few million per day in volume. It's not unreasonable to think they might still be solvent, even with a 30 million dollar loss. But they also might not. However, they definitely won't be if their fix to block the stolen Tethers goes through.
No. They blacklisted the stolen tethers, and all they now have to do is issue a new batch of $30 million worth of tethers. In no way this puts them in the red.
