There are exchanges (a lot of them, actually) that list USDT as part of a trading pair. Bitfinex, as I understand it, allows withdrawals in USD (modulo the restrictions above). From an end-user perspective, the only time you ever deal with tether is when you make a tether transfer. They are correct in not treating the on-exchange trading pair as BTC/USDT.
Just as when you deposit on any exchange, for example, Kraken, you don't have "USD" per se, you just have "Kraken USD credits" which you can withdraw, subject to their limitations, via wire transfer. Also, when you deposit your USD in Chase Bank, you don't have USD, you have "Chase USD credits" which you can withdraw, subject to their limitations, on demand.
In all cases you are dependent on the solvency of the institution, which is what is in question here. But Bitfinex is correct in not saying that you are buying or selling USDT -- you are trading with USD, regardless of what internal accounting practices they use to ensure that they are solvent.