FTX issued FTT to Alameda. We have no idea what Alameda gave them as collateral, but it's clear it wasn't cash. Lending is a form of investing. (I don't get what unlocked versus collateral FTX on Alameda's balance sheet means.)
Also, FTX minted FTT out of nothing - effective cost zero - so no matter what they received in exchange, even if they had received nothing that is not an investment unless they received Alameda equity. I agree that lending is a form of investment but nothing says that they received a loan in exchange.
You could still be right, but it's all speculation :)
FTT spiraled and FTX went insolvent.