In my state at least all a kid needs to do is one meet at the old level early in the season, get the qualifying score and then they are able to go to another meet a week or two later and be the next higher level. I agree that it would be hard to get a 32 at L6 w/o a robhsbt (floor would probably be really low), but it's not impossible if the other 3 were good (or at least 2 were in the 9's...two 9's a 7 and a 6 could easily hit the 32 mark).
Is the girl good at bars? If so, I'd suspect that is why they'd move her up as talent on that event seems to trump weakness on the other events more than anything else, and if her front tumbling and overall form is really good I can see that helping too. One of the other posters also said you *can* do L7 w/o back tumbling, and assuming this is true (I woundn't know myself), that would probably be even more reason to get her out of L6 (where you *have* to back tumble) and to L7 (where you don't).
I understand what you mean about how your daughter was pushed to get her score, etc., but I would never say something about this girl to them. It will just come across as your questioning their judgement and expertise, and no coach likes that...especially when it involves a child that isnt even yours. I'd advise just keeping your frustration to yourself. I'm sure we all see level move ups that don't make sense sometimes, but we need to just keep quiet and realize that they don't really affect our kids (if they are undeserved, the scores will show it).