It's not my interpretation, it's what's written. As to the number of hours point you raise, it literally says "nights" so if the guest is there for no part of a night, then the number of hours is irrelevant. It could be 1% of a night to qualify as a stay, but since OP spent an entire night or nights completely away from the property, they were noncompliant with that requirement no matter how it is interpreted.

I've pointed out, as a lay person, that I think the rules are pretty clear and that I never thought I'd get away with what the OP was surprised they did not get away with. But if you're a big, bad lawyer, then get a class together and stick it to the man.