How bizarre! I have known people who have shaved their dogs *against* veterinary recommendation just because they don't like vacuuming up fur, which does seem cruel. Perhaps that was her experience, too. But once you explained the vet's involvement I can't imagine why she kept on about it. And really, even if you'd said "Yes, my vet says shaving her is cruel but I don't care!" it wasn't the time or place to debate it with you.
I think you handled it very well and did the best you could.