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 to maintain its price, the most important thing out of them is its peg.
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).