Tether admits that most of their assets are made up of commercial paper (aka bonds issued by companies). Suppose the minted USDT was given to the companies issuing those bonds themselves, then to reverse this, you don't need USD. You can simply cancel the debt and burn the USDT without a single dollar changing hands in the entire process. But dollars do change hands -- as payment for Tether's service of continuing to keep USDT going so those corporates can exit cryptocurrency at some point, in the form of interest on the commercial paper.

If a major counterpart was Binance, for instance, Binance could offer no cash upfront, issue a bond for a billion dollars to Tether, accept USDT1bn in exchange, use USDT to buy bitcoin, sell the bitcoin as USDT1bn + profit (and convert that profit to e.g. USD), and hand back the USDT1bn + interest, & cancel the bond. That's essentially the running theory of Tether's operation. Money flows overall from whoever bought Binance's cryptocurrency, to Binance, and to Tether. And Tether maintains very little cash whatsoever, as there is no need unless everyone wants to redeem at once. And in this situation their plan is just to throw up their hands and say "we prioritise our customers" which is basically Binance and whoever their actual customers are, i.e. the issuers of commercial paper, not you.