"What was a woman doing with the Quran? Women aren't allowed to touch the Quran."
I'm pretty sure they are, actually.
Ah no. It is forbidden to touch or carry the Qur'an while one is in a state of impurity. Some scholars won't let women touch the Quran at all because they could be unclean. Some teach that women have to have the Quran interpreted to them.
The extremist intrepretations are followed in places like Palestine.