I think usdt was based on the fluctuations of dollar rate, and what I see about it's fluctuations is the same with fiat cash value or the stability of this asset. Once fiat value also rises, price for usdt also be affected that's why exchange to different coins would become profitable when acquire more gains in trading.
That is another reason for USDT could maintain its price, the most important thing out of them is its peg or reserve.
When someone deposits 1 USDT on exchange wallets, at the same time the exchange credits 1 USD to the user wallet.
Its stability comes from the USD reserve. It is pegged 1:1 to the real USD that is why it could maintain its price(we are not talking about a rumor it does not have enough reserve to back it, we are purely talking about its mechanism).
This true, my country stablecoins work like this too. The point too control the price is to have market makers too in the market to keep the price fluctuations not too high. Also, if the price too down like 1%, many trader would take that as opportunity because you can withdraw that stablecoins into fiat 1:1, otherwise if the price too high people will deposit their fiat and change it to stablecoins then sell it on the market.