Chances are that if the provider is upset about it, it's because it's disruptive to the schedule. The child probably isn't napping because they've slept in, or they're crabby because they were not fed before being dropped off, or perhaps the provider transports kids to school as part of their services and needs to know when kids will be arriving, etc.
I have no issues with late arrivals provided I know about it ahead of time and can plan accordingly. Usually it's for an appointment or something and then child was up at their usual time and fed before coming here. Otherwise my contracted cut off time is 9:00.
I think by the time a provider vents on here about it, it's become a Very Big Deal.
OP, I would have locked them out. It sounds as if it wasn't a good fit anyway so there you go. I only take kids whose parents are working - my families need to drop off by 8:00 so they're not late to work.