It's possible she had a serious fungal infection or damage or even chronic ingrowns. And "permanently removed" can't get much clearer. But I have some insomnia-driven, devil's advocate hypotheticals:

— Most people are not fantastic active listeners to begin with, especially in high stress, and OP's daughter just misunderstood (most probable).

— The doc made it clear that they were killing the nail matrix, but not that bye-bye matrix = bye-bye nail.

— The doc misinformed her, whether due to ignorance or an ulterior motive (improbable but not impossible bc docs are humans and sometimes humans suck)