I was thinking along the same lines. I went out on a semi-blind date once and we agreed ahead of time to split the cost of a movie. Well, when I got there, he refused to let me pay for my end and, also, kept trying to make moves on me the whole time. I kind of got the feeling that, since he was paying, he felt entitled to something. I'm not saying all guys are this way, or that even my date was. I just felt a little mad that I wanted to start out our first (and only) date in the friend mode and he wouldn't listen.
Also, it could be (and this is a long shot) that this woman once dated a man who accused her of being a gold digger or materialistic because he paid for everything. I had a couple boyfriends that did that to me so now it's very hard for me to let a guy buy me stuff. It drives my current guy crazy when I don't let him buy me stuff, but I'm working on it. So far, I'm okay when he buys me food, but the more expensive stuff is harder for me to get used to.
Anyway, just some thoughts. I'd say the best thing is to ask, but not probe too much, as to why this woman doesn't want to let you pay. That's probably the beginning to working out an arrangement that works for both of you. Good luck!