From their site:
> ¹ FDIC insurance applies only to the USD reserve funds. GUSD exist as ERC-20 tokens on the Ethereum blockchain; tokens are under the user’s self-custody, and are not insured through Gemini.
So if you send them USD, they'll hold your USD in an FDIC insured account. If you hold GUSD, and it turns out GUSD is a fraud or is otherwise insolvent, your SOL.
I don’t blame you for getting that impression, though. The Gemini dollar marketing page talks about earning high yields, and it talks about FDIC protection. It doesn’t explicitly mention whether you can get the yields and the insurance as the same time, but the answer is no.