Do they not have a school reading book, then, i.e. a book chosen from the school library? Either way I would interpret this as 20 mandatory minutes daily of reading homework, and encourage my DC to have a "school log reading book" and write down that as what was read each day, ignoring anything else s/he might read. I agree, extra reading for leisure is not their business, and they're probably only trying to check that some reading is going on. (In any case, my DS is one of those who leaves books scattered round the house and reads them in parallel, so it would be impossible to record in any sensible way!)
DS is in P4 which I guess is roughly 3rd grade, and the system is supposed to be that we listen to him read aloud and sign his book when we do. Each signature gets him a "Keen Reader Point". Last term he had the fewest but one of these in his class! Fortunately his teacher understands the situation. (He does sometimes read aloud and get one - reading aloud is a fine performance skill, after all - but in his case it doesn't have much to do with his ability to read and it isn't something I'm going to add to the list of things that should be done daily.) Come to think of it he also came home with a reading log booklet at the end of last term that seems to list only the books he read at school and kept there. I don't know if other children carry books back and forth between home and school. Maybe they do, and those are the books they read aloud to get their KRPs.
