I know of someone that did this. She was a governor of their local village Church primary school that her children went to.
Unfortunately due to lack of housing in the area as well as a bit of a dodgy reputation, the number of children dwindled and they were bordering on putting together three year groups in one class, which would have put my friend's 2 kids (3 years apart) within the same class. Knowing her own children as she does, she knew that was never going to work, so got them a place at a school in the nearby town instead and stepped down as Governor.
There was nothing wrong with the quality of teaching, it was just that the school no longer suited their needs.
As PP's have said, it could be an issue with the school, but more likely it's just a personal decision of the family. Keep an eye on the other school details and see if the parent pops up on their Board of Governors.
It might be something as simple as they preferred the other school in the first instance and were on the waiting list and a place came up. Couple that with a parent that want to be involved with their child's school to the point of volunteering to be a Governor while they're in reception, there's a good chance they'll end up on the Board in the new school too.
If it's something really bad I'm sure the parent will have contacted Ofsted, so time would tell.