I just think we need to stop judging so much and trying to fit people into boxes. If she thought she had a natural birth, then let her be happy with thinking that.
I had full epidurals with both kids, but with Nitara's birth everything else was natural. Do I consider it a natural birth? No, but I did refuse any other interventions (pitocin, episiotomy, early cord cutting) so I feel good about that, and I'm not letting anyone tell me I had less of a birth because I chose to have an epidural for very personal reasons.
I think if a woman can get through a birth and feel good about it and not feel that the medical staff took advantage of her or she was forced into things she regrets, it's a good birth! (Natural or not)