The official statement was just released. The article points out a few rule clarifications. First, about gaining possession of the football:
Rule 8, Section 1, Article 3 of the NFL Rule Book defines a catch:
A forward pass is complete (by the offense) or intercepted (by the defense) if a player, who is inbounds:
(a) secures control of the ball in his hands or arms prior to the ball touching the ground; and
(b) touches the ground inbounds with both feet or with any part of his body other than his hands; and
(c) maintains control of the ball long enough, after (a) and (b) have been fulfilled, to enable him to perform any act common to the game (i.e., maintaining control long enough to pitch it, pass it, advance with it, or avoid or ward off an opponent, etc.).
When a player (or players) is going to the ground in the attempt to catch a pass, Rule 8, Section 1, Article 3, Item 1 states:
Player Going to the Ground. If a player goes to the ground in the act of catching a pass (with or without contact by an opponent), he must maintain control of the ball throughout the process of contacting the ground, whether in the field of play or the end zone. If he loses control of the ball, and the ball touches the ground before he regains control, the pass is incomplete. If he regains control prior to the ball touching the ground, the pass is complete.
Next they present the rule for simultaneous catches:
Rule 8, Section 1, Article 3, Item 5 states:
Simultaneous Catch. If a pass is caught simultaneously by two eligible opponents, and both players retain it, the ball belongs to the passers. It is not a simultaneous catch if a player gains control first and an opponent subsequently gains joint control. If the ball is muffed after simultaneous touching by two such players, all the players of the passing team become eligible to catch the loose ball.
Ultimately, the argument here is that Jennings didn't have possession of the ball when his feet hit the ground, Tate did. So regardless of who grabbed the ball at the peak of the jump, the officials ruled a simultaneous catch when they hit the ground, resulting in a touchdown since ties go to the passers.
It is important to note a few other things about the statement. First, they acknowledged Tate should have been called for pass interference when he shoved Sam Shields. Second, the video review did not show enough evidence to overturn the touchdown ruling. This would indicate that had the official who called for a touchback was the one the referee listened to, then it would have remained an interception rather than a touchdown.
NFL.com just put out an article discussing the statement by the NFL on the play. The author mentions that the NFL doesn't overtly say the officials made the right call and there wasn't sufficient evidence to overturn the initial ruling:
The statement goes out of its way to say that Golden Tate should have been called for a pass interference. It does not say that officials were in error by ruling Tate and Jennings came down together with the ball. It also does not say it was the correct call. There was not indisputable evidence to overturn the call, according to the league.
Reading between the lines, the league seems to be indicating the officials may have made an error in judgement, but the judgement wasn't grievous enough to be overturned.