A colleague warned me of the same when I was having my wisdom teeth removed. As a result, while I was being put under, I was very focused on the effects of the anaesthetic. I feel about as confident as one can be that I was completely unconscious during the entire operation. I remember the surgeon asking me to count to ten, and the specific feeling of my vision melting and swirling around, before suddenly waking up with the surgery over.

When I wake up from dreams, even with no memory of them, I sometimes have "a memory of a memory"; the tip-of-tge-tongue feeling that there's something interesting I'd experienced, but which I now can't remember what it was. But with the anaesthetic, there wasn't anything like that at all.