Since the game was in Pittsburgh the scoreboard operators did not replay it on the video screens there. If the roles had been reversed you can be sure that would not be the case. I suppose you can call that home field advantage, but that seems to be a slippery slope right there.
On the other hand I did read somewhere that the play was not replayed on television because the Pats saw the TD was not called, so they hurried to the line of scrimmage. CBS saw that and decided to stay with live action rather than showing the replay. Kind of a damned if you do, damned if you don't situation.
This is one thing that I've never liked about replays, that sometimes coaches get to watch the replay and other times they don't before making the decision on whether or not to challenge. Similarly in one case the network may show a replay with a very good angle, and the next time show two or three replays with bad angles before finding a clear shot of what happened. Their broadcast shouldn't have an affect on a challenge, or the outcome of the game.
That whole concept just doesn't sit well with me, and never has. Unfortunately the only solution - don't show any replays in the stadium until after the time to challenge has passed - is simply not going to happen.