Tether was originally setup as RealCoin. It originally had a clear bank account relationship with a Taiwanese bank. It had about $30mm. Then the bank cut them off.
Since then they've been floating without any announced banking relationship and they also changed their terms of service. Over the same time period they made a partnership with BitFinex and their supposed AUM has gone up over 10x.
No one really knows how much of that corresponds to actual USD or if anyone can actually withdraw. A famous twitter account (https://twitter.com/Bitfinexed) points out every day the ostensible discrepancies between the supposed AUM and public amounts.
I'm generally a huge fan of the goal of Tether (a stable USD backed cryptocurrency), but the proof is in the pudding (i.e the reserves) and your access to it, and both of these are rather questionable.
Full disclosure: I know and am friends with some of the current Tether team and was recruited for RealCoin in the early stages of the project. They are working on a hard problem (asset-backed cryptocurrency on the way that gets the most traction in the market at present, not necessarily the way that inspires the most confidence.