I wonder if the girl is so independant she dresses herself and mom doesn't always know if she's wearing of not.

Mom probably doesn't see it as a big issue. But, your house, your rules. If you require underwear then she must wear it.

I find it more concerning that she doesn't have a full change of clothes in her bag in case of accidents.

I don't think you're over reacting. I think I'd be in shock if I had a child not wear underwear. It's like teaching them to not dress them selves properly.

So strange!