So in that theory they do get sufficient USD to cover USDT (as opposed to printing it out of thin air) but are using it to buy questionable CP.

I think many people believe they don't even have enough USD to start with, eg because some of their assets are loans collateralised by crypto (such as the Celsius 1B loan).

I believe both are true - Tether printed USDT against non-cash, and used some of the actual cash to buy dodgy assets for more yield.