Vitalik Buterin, the founder of Ethereum, published a post on coins like Tether a few years ago:
https://bitcoinmagazine.com/articles/mastercoin-a-second-gen...
My understanding is that unless there's a "tether-run", where everyone wants to get out of Tether at once and the company behind Tether isn't well prepared for it, then that's when the coin may actually crash. Otherwise, it will self-stabilize by putting more Tether on the market, or taking Tether out of the market. So in a way, I guess it works a little like the Federal Reserve.
As for not having enough money to "back Tether", this is bad in the sense that they promised they would, and they're not showing proof that this is true. However, it's "only" as bad as any real-world bank that uses a fractional reserve banking scheme. So just like a fractional reserve banking entity would crash as soon as there is a major bank run, similarly Tether would crash if they don't actually have 1:1 USD:USDT backing.
So Tether is about as "shady" as any of the major US banks - and yes, I would agree that both are pretty damn shady. But this seems to be the status quo right now, so if you don't trust Tether, I surely hope you're not keeping your money in a bank either, because I think we're getting close to another financial bust, and we'll go through the same crap or worse that we went through in 2008 with the defrauding banks.