Bwhahahaha!

I have two degrees, an AS in Nursing, an AA in Elementary Education plus I'm one course and student teaching away from holding a duel BA in Early Childhood/Elementary Education and according to those statistics I'm somewhere between the "no high school diploma" and "high school diploma" level.
But ... I am very successful! I love my job (preschool teacher) and wouldn't change it for the world, my job loves me, I love my family and friends, my family and friends love me, life is grand, end of story.
Aww, I feel bad for your daughter. Somewhere along the way she heard someone say that and that person probably got someone to laugh at the remark, so she probably thought she could get a laugh with it too. Then it backfired. That alone, without being attacked for the comment, is embarrassing enough. Almost every moment in a young person's life is a teaching moment. The adult that treated her that way is just wrong, wrong, wrong. It always amazes me when adults think they can treat children any way they want to just because they are bigger or older than them. I treat everyone, whether they're three, thirteen, twenty three, sixty three or eighty three the same way. I treat others the way I want to be treated. Some adults just have some sort of authority trip hang up.
On the other hand, I do think your daughter's remark was insensitive. I can't stand it when anyone's feelings are hurt because they feel they've been mad a joke of.

And hey, I went to college, three times now

, and I mess up too! Things happen.
I think I would talk to your daughter about that, and I would also let her know that that other woman was way out of line for the way she treated her and she shouldn't have treated her that way. I wouldn't make your daughter apologize to the other woman unless the other woman apologized to her first.

Adults are supposed to be the ones who take the high road in those type of situations. Adults need to be check their own behavior too.
Two wrongs don't make a right. That woman should never have reacted that way to your daughter. Your daughter's joke is understandable for her age and knowledge of the world (though insensitive to me), the woman's behavior is not.