I'd guess the 0.999 price just indicates more selling pressure than buying pressure. The market cap of USDT has been trending downwards over the past 2-ish months.
Bingo. Tether defends the peg on their Bitfinex exchange. Then people arb the difference.
But right now people are hesitant to arb and so need a higher premium.
In low confidence systems, 0.99 can cause a bank run and eventual death spiral.