I had to process these requests at a company I used to work for. They do send “proof” (proof in quotes because you have to believe in good faith they didn’t just make it up, which I have to believe they didn’t).
We never shut anyone off though. We worked with business exclusively and only ever sent “scary” letters. Though we had one client that was a major music venue (a very known venue that’s pretty famous) who would get these letters all the time. The irony was too much for me. I ended up calling them personally most of the time because it was too funny.