I'm skeptical that Bitcoin's value is strongly related in any way to Tether. The larger meta-Bitcoin point, though, is that although nobody can print Bitcoin at will (because it's open and auditable, unlike the printing of dollars) anybody can create their own cryptocurrency and print that.
On the other hand, everybody knows that, so Bitcoin's so-called "market cap" is several times bigger than that of all the other cryptocurrencies put together.
They're not counterfeiting Bitcoin, just the means to prop up it's value. The big difference is the printing of Dollars is open and auditable.