I don't think that's a counter example. Our day care requested sick kids to be picked up within an hour. A single late pickup of a sick kid due to traffic/distance would be handled normally. An unreachable parent who turns off their phone and is extremely delayed, especially on multiple occasions is a very different thing.

When we looked at in-home child care, one of the options was a nanny who would care for kids even when the kids were sick. So I'm sure the rapid-pickup-of-sick-kids policy isn't universal. However, our day care had that policy and we made sure we knew who was "on-call" to get kids when important meetings or work travel impacted our availability.