It's actually almost never exactly at $1 and the reason why it's immediately pegging back to $1 is because there is an arbitrage opportunity, assuming there is enough backing so that in the worst case the custodian would just buy back the tokens for exactly $1, no matter what the market price is.
Seeing USDT at 0.97 temporarily doesn't mean much more than there is an insane amount of money exiting right now. One exchange can quickly fall to something like 0.97 if there is not enough buy power closer to $1