I'm not sure I would say you are being bamboozled by this developer, but she certainly does seem to be going on an ego trip. From what you described, she seems like the majority of small time web developers out there who believe they can do no wrong. I used to see it on a regular basis when a developer would insist on using their own custom CMS. These days it's their own custom WordPress theme. Same idea.
You haven't really described the environment or the hierarchy of your relationship. If you're ultimately responsible for this persons work, do you also have the responsibility of managing them? If so, can you step in and rattle her cage a little? Let her know that this is your show and you do things a certain way. You don't need to be rude about it, but stay firm and make sure she understands that you are responsible for maintaining the code moving forward.
Asking to see documentation, while most developers don't create their own documentation, isn't unreasonable. Requesting to see the code is even less unreasonable. You were within your rights and even sensible to request these items. I personally wouldn't move forward without seeing the code.
Maybe you can meet her half way. Tell her that you would like to start with the default WordPress theme, which is very powerful in its own right, and develop from there. This way you know that the theme is built on a solid foundation and she still has the freedom to extend it as she's comfortable.
If indeed you are not the manager in this situation, it sounds like you'll need to get that person on board and very carefully describe the situation along with the risks. Be careful not to bash this developer or put her down in any way, just voice your concern that the code may not be stable or maintainable given that you haven't had the opportunity to review it. Without this guarantee, you may not be able to maintain the project after this contracter has left.
Stay calm, be objective, but most of all be firm in your expectations. You're on the right track.