I don't believe that is the case, and I think you'd be hard-pressed to find it in the rulebook. From 2014:
Article 3 Completed or Intercepted Pass.
A player who makes a catch may advance the ball. 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.).
Note 1: It is not necessary that he commit such an act, provided that he maintains control of the ball long enough to do so.
Note 2: If a player has control of the ball, a slight movement of the ball will not be considered a loss of possession. He must lose control of the ball in order to rule that there has been a loss of possession. If the player loses the ball while simultaneously touching both feet or any part of his body to the ground, it is not a catch.
Item 1: 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.
The "act of catching a pass" is fulfilling a), b), and c). As c) must come after a) and b), a player who goes to the ground at any point in the act prior to having fulfilled c) is required to maintain possession throughout the process of contacting the ground. There is no mention of being able to satisfy the requirements of c)
AFTER a player has been determined to be going to the ground. You're either in the process or you are not. If you are, then you need to maintain complete control. The rule cannot apply to a play and be negated after it's application.
Once the 3 prerequisites are met, the rule cannot be applied to a player who goes to the ground. It's only applicable to players who are going to the ground prior to meeting all these requirements. Additionally, once the rule is applied it makes not one bit of difference as to whether or not a player had complete control prior to going down or whether or not the time for a football move was afforded to him. The only thing that matters in determining if the pass in complete is whether or not the player secures possession without the ball hitting the ground in the process.