The problem is that unless you claim CB, there is often no paperwork at all that demonstrates that the child
lives where they do. About the only things are a Building Society account that might have triggered an annual statement of interest or a NHS medical card. (Hardly anyone can ever find the latter, or so it seems!)
Otherwise it is all over to evidence that the parent is resident at the address. Council Tax bill, house purchase documents, utility bill, bank statements, etc.
The only time it gets difficult is when the parents are separated and there is a need to establish exactly where the child is resident. That is when a CB letter is always helpful.
If they start getting funny with you, just offer to go into the school with your full files of personal paperwork so they can see anything they wish to.
(Cross-post with greengrass, who can find the Medical Card!