Welcome SuzieT and don't worry you are in the right place, may be an 11plus board but covers all sorts of school happenings these days.
I have heard of this sort of thing happening before in indies and I find it very annoying - where I lived it tended to be the indie preps with good results and longer waiting lists - parents tended to feel relieved or honoured that they had a place - I'm really not sure which !
then comments would come out about people being "asked to leave" ... suggesting they took entrance exams to year 5 and 6 at other indies (also non selective), often done on the basis that "if they get in now then they won't have to take a test to get in there at year 7..."
Question is - what do you do? I would be tempted to turn it round and suggest that the HM advises you on schools and does the legwork with the schools .. you have obviously already contacted them and have no joy. See what the head finds when she tries...
re your DD - difficult for her - you just have to make sure she keeps her confidence up and does not get wind of this and get upset. If the school do comment to her - make a HUGE fuss. Other options would be to get her assessed by someone independent - DCs prep used to do this - good on all counts.