Interesting. A case were my observation doesn't match reality at large. Where I live the private school teachers seem relatively well compensated. But I live in a mecca of sorts for private schools (Dallas's "private school corridor")
Seconded, the main draw is a better work environment and free tuition.
Assuming the school's good (the majority of private schools aren't, really) that is absolutely one of the main perks. Free or reduced tuition can end up, effectively, being most of your compensation, especially if you have more than one kid going.