Yes this is the crux of why SBF is in trouble; they used customer deposits (whether BTC, fiat or shit coins) to compensate for their failed PE investments (in order to keep it afloat) with the hope that their PE would make enough money in the future to pay back the customers when the customers withdrew funds.

In some way, this isn't too different from Fiat banking; the repeal of Glass-Steagall resulted in banks being able to invest customer deposits into risky assets. What resulted was a bubble in complex securities (mortgage-baxked securities & credit default swaps) which led to failure of some banks. The only difference is that the Gov and Central Bank effectively paid for the losses that the bank received - creating a precedent that risky investment of client funds are acceptable with limited repercussions.

Since 2008 this trend in risky investment has continued (in both Fiat and crypto worlds) as fund managers are looking for yield. A decade of artificially low interest rates have effectively forced funds to gamble to produce some returns.

EDIT: regarding people buying and selling Bitcoin on their exchange, this was possible because FTX had legitimate liquidity on their exchange to support normal deal flow. It was only when there was a run on the exchange that they became illiquid and then insolvent