Yes you need a negative result on the test to return to the United States, but you never know the sensitivity of the test you are taking. It should be from an “approved provider,” but what does that mean? No authority from the United States can readily verify how good the test is.
Let us say you are a hotel owner, which kind of testing service do you wish to commission to send around to your rooms to test your American guests? A highly sensitive test that will yield periodic false positives, or a not very sensitive test that won’t generate false positives and might even result in some false negatives? And say some of your guests truly will be Covid-positive — do you wish to keep them in their rooms for another week or two, with all the attendant risks, or do you wish to send them along their way?
You don’t even have to imagine that the hotel owners are entirely cynical. They themselves can’t judge the accuracy of the tests, so a service that yielded a fair number of Covid positives could be seen as “they make too many mistakes and won’t let our guests leave, we don’t want them.” If the Delta variant is outracing publicity about the Delta variant, as was the case for a while in Tulum, such a hotelier reaction might be all the more likely.
I did in fact test negative. And the testers were very nice to me.