This is not accurate. The ToS for FTX explicitly said that customer funds would not be used for investment purposes. While it didn't explicitly say it wouldn't be used for lending, it was a broad assumption in the industry that the exchange was solvent and could back user assets on a 1:1 basis.
It is widely believed now that Alameda went deep underwater during the collapse of the Luna ponzi (this one was quite literally structured like a ponzi) and borrowed a large amount from FTX to bail themselves out of it. In the wake of this, FTX had a shortage of hard assets and a fat bag of FTT that the loan was issued against, which is what exposed them acutely to a bank run and/or price decrease in FTT.