That is rough for a 6 year old, for goodness sake!
It is getting silly with private schools - if the peg doesn't fit, they throw it back to the parents. I suspect she was worried/cried, so they judged her on that. Some schools really really can't be bothered with a child who may possibly need a single seconds more attention than the average. Some are great and have fantastic, loving staff.
Nohing wrong with the child, just the school wasn't right for her.
Tell her that you, her parents, had decided that you didn't like the school and it wasn't right for her. Don't tell her that she in any was failed to make the grade.
I would ask for their decision in writing. Don't get angry, upset or defensive because, to be honest, they really don't give a rat's about you. You've had a lucky escape - if they really think so little of bothering he help settle a worried child, they their pastoral care is woeful. If you feel particularly peeved, write a letter expressing your dismay at her treatment/handling. However, do remember that staff chop and change on a termly basis so you never know where a head/teacher will pop up. Its a small world!
I am finding that I hear more and more stories about such money-making factories that just would happen in the state sector. They often play by their own rules and can treat people with utter contempt.
Find a school that is reccommended by parents. Im not sure where you are but if you give a rough location, I'm sure people will have some good stories to tell.