Like Wyler, I was also a Parent Governor whilst serving, and I agree with most of the points raised.
This will be another stab by central govt to show that league tables work, and that they are indeed taking the concerns of service parents into account by creating a database that shows if service children are indeed adversely effected by moving schools.
It will as always achieve nothing except to provide an accountant somewhere sufficient information to statistically prove that there is no longer a need for BSA.
As for the schools, they will go along with it because there is quite a lot of money to be had from LEAs if they can prove they are "Garrison Schools". Although these were officially phased out years ago, if the school can prove that (figures from memory only, so please don't quote as too accurate) more than say 60% of their student population herald from service families, then they are entitled to up to 40% more funding per year.
As my kids school shared a fence with my station, this type of census was never instigated because 85% of the school catchment area was MQs (or SFAs now) anyway. I can see why some schools would want to know though.
I personally would return it incomplete, or not at all, just like the infamous "ethnicity" forms.
As for whomever it was questioning your right to approach the Govs, that is what they are there for, especially the Parent Govs. To bring the concerns of the "Parents" to the full board. The clue is in the name really.