Somewhere along the line, somebody interpreted "goes to the ground" as meaning "starts to fall." That brought in the whole idea of maintaining your balance, which has nothing to do with making a catch.
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 until after his initial contact with 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.
Look at the very next item in the book, Item 2:
Item 2. Sideline Catches.
If a player goes to the ground out-of-bounds (with or without contact by an opponent) in the process of making a catch at the sideline, he must maintain complete and continuous control of the ball until after his initial contact with the ground, or the pass is incomplete.
What would it matter what a player was doing if he was already out of bounds when he started to fall?