Only anecdotal evidence. I had my account shut down in this way, BayAreaCoins had their account shut down in this manner and there are many others that I'm unsure if they'd be excited about me sharing their name have been in private conversation with me about their parallel experiences.
They used to send a message like this
"Hi there,
Due to a recent account review, Gemini has determined your account must be closed. Unfortunately, we are not able to elaborate on the specifics for this decision.
If your account contains a balance in USD and/or Bitcoin and/or Ether, you will have 5 (five) days from the receipt of this email to withdraw the entirety of your funds at which point your account will be closed.
If your account is closed and a balance remains, please email
support@gemini.comOnward & Upward, Gemini Customer Support"
At least allowing some time for withdrawal, but recently they've been restricting accounts and funds without any such messages. They were making requests of their customers such as producing 3-months of bank statements for the associated bank account. They were requesting KYC documentation and then still restricting accounts after such documentation was produced.
Long-Story Short, I don't really have a source, but I've been affected personally and I know many others that have as well. I lost an insignificant amount of coin, but there are others that have lost much more.