Lisa, I think there's just a miscommunication there--you're saying the same thing. It's the provider's liability insurance that's the problem, not the patient's health insurance.
As for the couple in BoBB, it could just have to do with the structure of their insurance and how much they're expected to pay. I don't remember that portion of the movie (I only saw part of it) but that doesn't mesh with any insurance I've had. Were they planning a home birth? If you transfer from a MW to an OB in labor, there's 2 sets of charges and it can result in you paying more (you still need to pay the whole midwife fee but now insurance won't pay it), whereas with ERCS, you're with the OB from the get-go, one charge.
I've not heard of a health insurer preferring RCS. It costs them more; they have to pay for an OR, anesthesia, the procedure, a longer hospital stay, and potential complications. If a VBAC goes wrong, they have no legal liability, just a bigger claim. They don't want to push one or the other for PR reasons, but from a bean counter POV, there's no reason to deny VBACs: if it goes well, you pay less, and if it doesn't work, you pay for the RCS you would have anyway. Complications will always occur in either scenario, but I don't think the extra complications from VBAC-turned-CBAC are significant enough cost-wise.
Liability/malpractice insurance is a different beast. From a liability POV, RCS is the more economic option--the dictum is, "You only get sued for the sections you don't do."