It's not unusual for parents to start attending church, just to get their kids into a "good" school, which happens to be a faith school.
It's no different to people who move house, so they're in the catchment area of the school they want their child to attend. I suppose parents just want the best for the children, and will do whatever measures necessary to make that happen.
I didn't think it was like this with COE schools though? My sister's kid goes to a COE school and neither of them go to church, or have any intentions of doing so. I appreciate all circumstances are different though.
Does the vicar have to sign anything? The priest at our church is pretty clued up on it (like they all are no doubt!) and won't do it. You have to attend mass, regularly go to church, and then baptism, therefore it's not possible for someone to come in 4 weeks before they put in a school admission and just try to blag their way in.
You're right, in that it does then go to distance from the school.
You can also appeal if you're not happy with the school they give you and you'll be put on a waiting list.
Did you put more than one choice down?