It’s ridiculous, its enabled by default on any new device you set up and sign in to. I could have missed turning off iCloud on my iMac, but I didn’t have any problems before updating it, and then after I updated it I had iCloud full notifications, so I’m pretty sure it was off.
In this case though, it’s not a hallucination, there’s nothing false in that response, it just completely misinterpreted what the user was asking.