Yes, I've had random people show up on mine, like my then-current gynecologist--no, I don't want to friend her, thanks! Or other T's at ex-T's/ex-MC's practice. It made me wonder if Facebook paid attention to locations (I have location services on when using it) and suggested people from the location where I'd been. This was maybe 5 years ago, and it hasn't really happened since.

It's also possible that there could be friends in common, though I often get suggestions where no common friends are listed. The algorithms are pretty random, it seems.

I can understand a T blocking a client, though I'd also feel bothered by it. I felt sort of weird when Dr. T's wife posted in a group I was in (I was in it before I started seeing him, had no idea she was in it till she posted), and I let him know. She then left that group and apparently deleted many of her posts first. I felt strange about that (particularly that she felt she had to leave a group because of me), but it would have been posts about their son, so I completely understand why she did.

I don't know that she blocked me--to do so, Dr. T would have had to disclose my identity, and I don't think he can ethically do that. I mean, I guess if she let him into the account, he could do that, but I assume someplace you can see names of people you have blocked, and she might be like, "Hm, why is this LT person blocked? Oh, maybe she's the client!"