This is the correct answer. FDIC insurance is needed because when you give your money to a bank, they turn around and lend it out to other people, so when you want to withdraw they may not be able to collect enough to pay you out.

I suspect when you deposit 10 BTC in Coinbase, they actually just hold it for you. Honestly, given how volatile Bitcoin is, and the general upward trend, it would basically be insane for them to try to invest it in any other assets.