I assume that the USDT holding of the big exchanges are on behalf of their customers. I those customer begin asking to convert their USDT to USD, that could be a massive run.
"So you have this Monopoly money backed with a real dollar?"
"Yes"
"Can I see the dollar?"
"No"
So if a well-capitalized arbitrageur can buy a million USDT at a price less than 0.999, they can redeem them for a profit, as long as Tether keeps honoring redemptions.