Tether probably started exactly as they describe. At some point someone got a smart idea that just storing that USD in bank accounts is stupid, let's invest that to something more profitable. BTC is quite obvious choiuce of investment here.
All is good until someone figured out that if BTC goes down, we are technically insolvent.
Luckily there is a way out, as long as there are people taking USDT at its face value. Keep on printing USDT and using that to purchase BTC so that the price stays high/goes up. There is a limited amount of BTC, so there is a backstop here, you have all the bitcoin of the world as your assets and amount x of USDT on your liabilities. At that point you can say that hey, if someone wants to convert their USDT to USD, it is easy, just buy some BTC with maybe 1 million USDT/BTC, and by the way, our just opened USD/BTC currency pair seems to trade at 999 000 USD/BTC, so you can convert your money that way.
And USDT holders did not even understand that they were fleeced badly, but just should have kept their BTC investments in the first place.
Now, admittably, there is a small catch in this plan. What if people lose trust on USDT? Well, god news is that at that point, USDT issuer has on their accounts a significant sum of BTC (and unless they are complete idiots), a significant sum of USD. So it is likely that they figure out a solution for themselves that may include linving rest of their lives on some remote paradise island. USDT and BTC investors, then again, may not be so lucky...