In short, the idea comes from Kipling that animals observe a sort of truce around watering holes and prey animals do not have to be on guard (as much?) from predators in the vicinity.
I have read that this is false, that predators might even wait around watering holes for prey. However: Cleaning stations in the ocean seem to have rules and a truce (and a fish violating these rules, primarily not to attack other fish waiting to be cleaned is attacked by other fish of various species). So the idea of a truce at waterholes, perhaps only partially observed, is not that far fetched.
I wonder too if lions, for example, at some level understand that in order to survive they need prey to be able to eat/drink and breed. While this also sounds too sophisticated, is it any more sophisticated than the behavior of killing cubs so that females come into heat?