Bitfinex originally denied relation to Tether but it's been proven that was a lie.
The worry is, at some point there could be a "run" on Tether, when the curtains are pulled back, where all the USDT-BTC traders who happen to have USDT holdings and they suddenly become worthless because nobody wants to trade USDT-BTC anymore at 1-1.
As long as "public confidence" in USDT continues, the charade will too
It's hard to analyze Tether/Bitfinex's risks here because, well, they have been fairly opaque about what their actual financial situation is, so people are relying on their gut instincts to guess what it is.
The market cap for BTC is $1000bn. Wouldn't they easily be able to unload the position over a 1-3 month period without too much price impact? They own 1 percent of the market cap, and in the stock market we often see larget stockholders than this unload their whole position without a catastrophic impact.