Gyms do all sorts of stupid (IMO) things to make team more selective. Age limits, height limits, body type restrictions. It goes on, and it's maddening. You can't change their policies, though, and it does seem that your DD will not suddenly become team material in their eyes. Even getting an answer as to why from their cagey behinds won't change that.
I know you say your DD hated the other gym she tried for summer camp. What about it did she dislike, and is their camp indicative of the actual gym experience there? Was it the facility, the coach, the other girls, the hours, the intensity? Summer camp can be pretty different from team practices. Also, sometimes girls will dislike new gyms at first just because they are really different than what they are used to, but after settling in they will end up loving the changes.
Where I live basically everyone drives at least thirty minutes for gym (even for rec), and some much farther than that. If you want your DD to have a shot a team you may need to broaden the acceptable commute. As for her rec classes, I second the kudos to that rec program. My YDD was turned away from a rec program once because her skill set was too high. It's been our experience that rec programs don't advance to team level skills, so things like flyaways and BWO on beam would never have been taught to my DDs in a rec class. At least she is apparently getting solidly progressive training.
Also, you say she has all the L5 skills. Is that on every event? Some gyms will base levels or team invites on one event. My YDD had much more than all the requirements to be invited to team on three events, but just couldn't get the requirements on bars- she never got an invite. My ODD could just barely make the minimum requirements for all four events and was put straight to team.
