Like any good ex-prez (lol), let me break this tie...lol... Just kidding. Here, however, is my take on the subject.
It is a very fine line we all walk regarding our Principals. The truth of the matter is that it depends on 1) Your bylaws 2) Your membership 3) The Principal themselves and the relationship your board and/or membership has with the principal 4)Whether or not your principal is acting as a principal or as a parent with a child in your school, or both. Remember, each school, each principal, each board is different. What clearly works for Chrystal, obviously does not work for Lacrossmom. At our school, our principal operates both ways... she is the parent of one of our about to be third graders, and like any other concerned parent, has a right to a view, and a vote, just like any other parent. She has requests on behalf of her position as principal, and on those issues, she doesn't vote. Not because she can't, won't, should or shouldn't, but she knows she too has to walk a fine line and holds herself to a higher calling if you will (calling, for lack of a better or more appropriate word). Would our membership go in for her as a signature on our account? No. She has a vested interest in most of the financial outcomes. She also has her own budget, albeit, the school budget.
Can you exclude the principal from being a PTO board member and still have a good PTO relationship with him/her? Yes, but it may take some work. My thought here is that the principal probably shouldn't be on the board, mainly because, as we all know, your membership has more power than the exec board (in most cases). I would think they would have more power by operating as a member of the PTO body, than as what COULD be considered a conflict of interest by being on the board. Again, that is my personal opinion.
I will say this: My relationship with our principal is such that we discuss everything anyway, asking for each other's opinion as friends before even before something becomes a consideration for PTO. If we both thought something was a good idea, we explored it further as Principal and President, both falling into our respective roles. Most of the time, we both agreed on items and backed each other at the meetings. My most hated job in PTO? Disagreeing with the principal...lol... Just kidding. We both knew our jobs, and we did them correctly, although not always in agreement.
Good Luck