I had a dentist explain to me the same for getting my wisdom teeth out, as if it was a selling feature. At least for me, having my memory wiped is far more scary than just being put unconscious (or having some pain and a local anaesthetic).
I was one of the last if not the last patient the dentist who took out my wisdom teeth gave general anesthesia to (at my request, he was normally only doing local). Afterwards, the whole dental office staff (and my mother!) entertained themselves with having conversations with my incoherent self as I came out of the anesthesia. Apparently, I declared that I was ruined and would never be able to sing opera again (point in fact, I had never sang opera before).
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.
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Had a few eye surgeries (vitrectomies) under sedation, no pain but lots of flashing lights and lots of kaleidoscope patterns. It was pretty wild.
I was lucky that coming out of sedation was actually fantastic, like the only time I can remember feeling that blissfully relaxed was in maybe a few beach holidays I went on as a kid.
General anaesthetic scares me way more.