The Dalton School is private. They will probably be willing to juggle a variety of credentials and qualifications if the candidate is appealing. Don't let the experience statement deter you from applying...the worst that can happen is that your application isn't considered. It's not as if there's a fee to be paid
I interviewed and was accepted to teach there twenty-two years ago, but the commute from my home at the time would have been two hours each way, so I declined. (A few years earlier, I had lived only four blocks away and would have loved to accept the offer if it had occured then.) They were rather aggressive about it though, and I had to be very firm about not accepting. When they want you...they really want you!!