It's not a 'theory' at all. It's true by definition.
As long as the test can correctly detect positive cases, and positive testers are refused boarding, testing cuts down on the total number of positive cases aboard the ship.
By the way, I'm amazed at how many people fall for the argument that 'if there's still covid cases after X, that proves X doesn't work' -- whether it's vaccines, masks, or testing. These precautions work to reduce the probability of spread, they don't eliminate it.
Yes, some people will have covid but not test positive until after they board. Some people will get covid ashore. None of that means that precruise testing doesn't work to reduce the number of cases aboard.
As I said earlier, the key question is how many people are denied boarding due to positive tests. I'm hoping that one of the TAs here knows (and is willing to say) roughly how many boarding refusals there are.