The price of a USDT is 1 dollar. They give out new USDT for $1 a piece.
Sure, they may be spending these dollars elsewhere, thus holding a fractional reserve. Sure this may illegal and get them in trouble.
But this doesn't effect the dollar value for which these USDT's and thus Bitcoins are traded.
As long as a USDT is $1, nobody is manipulating the price.
If this were the case, Tether would be back by cash. But it isn't: they claim it's backed by cash, cash-equivalents and receivables from loans, including loans to affiliated entities (or some similar language).
So, for example: they could create 1M USDT and immediately loan it to their associated crypto-hedge-fund (for zero interest). The hedge-fund promises to repay that loan in USD (creating 'reserves' for USDT), and immediately places buy orders for Bitcoin; generating demand for Bitcoin that will raise the price.
The entire narrative around BTC is "HODL", and the only thing people really do with it is buy and hold. Money is flowing into the system, so there's room for scams to operate undetected within those margins.
They largely can't (especially that a good fraction of Bitcoin is now held by institutional investors). But it makes up for a good story.
That's circular logic isn't it? USDT is $1 USD and $1 USD is 1 USDT, therefore it is "stable".
That sentence in and of itself is meaningless.