I just wanted to add my 2 cents on the private school issue.
I attended parochial schools from 1-12 grades. They were considered (and still are) to be the best schools in our town. And in fact, I think that in many ways they are superior to most of our regions public schools.
HOWEVER, don't make the mistake of equating "private" or "religious" with no bullying. I was picked on a lot. Never hit because I was a girl, but lots and lots of teasing, name calling, social stigma, exclusion...
This continued all the way up until I graduated from high school. It was not fun & I will not be sending my child to those schools either.
We will homeschool because I simply see no other acceptable alternative (there are no charter or Montessori type schools around us either), but I totally respect that you're not comfortable with doing it. Just wanted to point out not to assume that private schools or schools in other areas are free from these problems. Frankly, I feel that if you are going to send your child to ANY sort of formal school they are going to deal with this at some point or another. But the faculty's response can and will vary widely from school to school and that should be what you focus on when interviewing people.
Oh, and my first questions to the principal would be "Why in the world do you feel that just because the boy's mother hit him in front of you the issue has been dealt with? Where do you think he probably learned to hit in the first place? Do you seriously think that hitting a child is an effective way to teach them NOT to hit?" I would also be asking for a meeting with the principal and the teacher who told you he "fell" to get to the bottom of that.
At the very least you should be able to find a school where the faculty doesn't *condone* hitting, which I'm sorry but that's what they're doing! If you do look into other schools in your area I would ask them what their response would be to a child's parents hitting them in front of the principal as a way to punish them for bullying someone. That right there should be a good indicator if you want to send him there or not.
Best of luck. Keep us updated!