In this web site we always draw the distinction between what you can expect traveling on your own or with a ship-provided (free or at a cost) tour.
With a ship's tour you have the guarantee of them always being on contact with the ship, and if there is an emergency the ship will not leave wwithout you.
Now, that is provided you don't do something silly. One couple on the first cruise (I think it was Carnival
) heard these same words, and thought it meant they could "disapper" at Atlantis in the Bahamas for over an hour after tje van was due to return to the ship.
The van waited and waited, and when they didn't show and the actual departure time nad arrived for the ship, the ship (which was in contact with the tour) advised them to return to the ship without them.
The lost couple missed the boat (in more ways than one), and leter said "Well, we believe we are due compensation because we were told the ship would not leave without us if we take a ship-sponsored tour."
Actually, I am not sure the cruise lines say that, it is just something known to cruisers like us - that the concept applies if the tour has trouble - but not if a newlywed couple decides they want a little extra time in the hot tub.