According to the OP, this is a very large facility with four barns. I assume the workers who come in during the closed day may not be terribly experienced (or are only being paid for a specific minimal number of hours work), so the logic is there may be concerns about everything getting done properly, or while one horse needing supplements and medication might not be a big deal, if every horse needs an extra “dump” in the bucket, plus a quick check to make sure it’s correct, plus extra blanket changes, the time adds up, labor-wise.
Ideally owners should be “allowed” to at least administer medication, supplements, and do a blanket change even when the barn is closed. I understand the total closure is in the boarding contract, but it can be hard to predict if a horse’s daily medication or dietary needs change. Of course, before BOs jump on me, I know that the “allow boarders to get in and get out to do a quick check and make up a feed bucket on Monday” exemption can be quickly ruined by one boarder who comes with her five unleashed corgis and decides to do a special grooming and photography session blocking the aisle as well as feed supplements.
I’m glad the OP is off the hook and a groom could be paid to satisfy the boarder’s horse’s needs.