It wouldn't bother me at all if the school board member had NO children, but I wouldn't vote for someone who chose to send their children to private school --it does seem elitist, as if they want to tell "the little people" how to do things, while they go do their own thing. I'd wonder WHY they wanted to be involved in public schools if they didn't want their children in them.
However, I can tella similar story that doesn't have any strange underlying motives:
I used to send my children to private school when they were in the lower grades, but I've always taught at a public high school. Why'd I do this? Simple: I wanted them to start out in a Christian environment, and I knew that the school they were attending had a solid phonics-based reading program, while the public schools were using a combination of sight-words and holistic reading. I wanted them to have that solid start. Also, originally there was a very practical reason: We could have the oldest attending kindergarten on one end of the building while the youngest went to day care on the other end. It made drop offs and pick ups much easier, and that was worth a great deal to us.
BUT I always intended that they'd transfer to public school well before high school -- before they reached my school. I wanted them to have the benefits of more honors classes, more languages, a more diverse student body, more clubs, more travel opportunities . . . and that's exactly what we've done.
I think we've given our children the best of both worlds by handling it this way. But that's not really the same thing as the school board situation.