It's a lot easier for me to assess the Mayo Clinic's website being legitimate than an individual YouTuber's channel.

I don't think anyone is talking about "medical sites" but rather medical sites. Indeed "medical sites" are no better than unvetted youtube videos created by "experts".

That said, if (hypothetically) gemini were citing only videos posted by professional physicians or perhaps videos uploaded to the channel of a medical school that would be fine. The present situation is similar to an LLM generating lots of citations to vixra.