'America's Cowboy' - the photo in your post proves you are wrong. Prescott leaves the game with more than 6 minutes left in the 3rd qtr. The Cowboys lose the lead, then gain it back - both happening with Dalton at QB.
The sports world and its followers for a long time compared quarterback starts in football to pitcher starts in baseball ( which shouldn't be done, in my opinion -but that won't ever change).
Since it continues to be done, however, we shouldn't attribute the win over the Giants to Prescott. He left the contest with the lead; but just like a pitcher- if his team gives up the lead in his absence, the game's outcome does not go on his record. The win or loss is awarded to a relief pitcher.
But by football standards, Prescott was the quarterback that started and played most of the game, so he erroneously gets the win put on his "won-loss" record.