I think there's a nuance here that's difficult for me to express. Explanations aren't wrong - not having a good reason to break the rules is wrong. The nuance is: what makes a good reason?

Your situation isn't a contradiction or counter to what I said. You have a different perception of persistent. If they were late for school every day because the bus never ran then you would presumably tell them to get the earlier bus so that they didn't miss an hour of school every day? Or if that was impossible you would discuss it an agree different expectations. This alters the definition of "late". You wouldn't simply accept that they are late every day - that would be irresponsible and make you a poor teacher.