Actually, recently I heard an interesting idea mentioned by a commentator (forgot who it was) about Hawk-Eye. Hawk-Eye has a margin of error. Currently, we use the Hawk-Eye system assuming that it is always correct.
A better way of using Hawk-Eye is as follows: A call is made on the court. A player challenges it. They should use the Hawk-Eye. If Hawk-Eye can answer with absolute certainty, then use the result of Hawk-Eye; if not (i.e., if the ball could be either in or out both being possibilities based on the margin of error), simply retain the original call made on the court (sort of like what happens in NFL; if you want to change the ruling made on the field based on a video review, it should be demonstrable without a doubt that changing the decision is justified).
Finally, many people think that Hawk-Eye is actually using the video that it recorded. No, it does not. It actually calculates (based on the trajectory of the ball and based on available videos taken from different angle) the landing spot of the ball (when direct evidence is not
available).