There are TONS of things that have gluten in them that you wouldn't think or be aware of. One of my best friends has a husband with celiac disease, and his mom is really bad about not telling him all of the ingredients. He's gotten sick many times eating her cooking, and it's so unpleasant and painful for him.
I've made food for them each time they've had a new baby, and I make certain to ask them ahead of time about each ingredient and show them boxes of things I'm making. Even if it's not typically something that would contain gluten, I look for a brand that guarantees that it's gluten-free, as it may be exposed to it in the factory or something. It may be that she is concerned that you will inadvertently use something that will make her sick, so she'd rather not chance it. Don't be offended! Like you said, people with celiac disease can get REALLY sick if they are exposed to something they are allergic to!!!!
I would just ask her if she's comfortable having you cook for her, and then if she is, show her the exact recipe and double-check each ingredient. Tell her that you will use one of those disposable pans that you buy to bring people food in. Let her know that your concern is for HER feelings and HER safety, and don't be hurt. It's nothing personal against you!!!! I'm sure she appreciates what you're trying to do for her.