It sounds like exchanges are using Tether because offering to cash out USD can be difficult if the exchange isn't in the US, so they let people use Tether as a proxy USD. e.g. If someone thinks the market's about to crash, they can sell their Bitcoin for Tether, then buy back Bitcoin when the price drops.

So if your coin has the same use case as Tether does now, people may not buy MyTetheredCrypto off you directly for USD, but they might buy it off you for Bitcoin or other cryptocurrencies you accept if it's not easy for them to convert to USD. Then you sell those coins immediately for their value in USD (you presumably having more access to do this than the buyer does) so you have your USD-backed tethered cryptocurrency with every MyTetheredCrypto backed by a real dollar USD.

Obviously I'm not really suggesting all this seriously though, there are lots of potential problems all over it.

The big problem being how you convince people to put real money into the system in the first place, especially if you want to keep the price fixed at 1:1. You end up with a huge quantity if BTC chasing tiny amounts of real USD. In a proper market the exchange rate should plummet due to the imbalance.