Not contradicting her is one thing, but actually acting on her advice, that you knew was wrong, just to avoid confrontation is a whole other story. I hope you simply didn't correct her, but treated your daughter's bloody nose the way you know is best.
I would have no problem telling someone with a smile, "Thanks, but her doctor has actually told us to do it this way.". For your children's sake, so they learn how to speak up for themselves, for others, for what's right, please try to find that polite, but firm voice. We teach by example, remember.