He dove for a catch and his momentum brought him out of bounds. That is not even remotely a case of a player giving himself up.
He did not declare himself down by falling to the ground. Yes, he fell to the ground but not in a manner by which he was declaring himself down.
Define for me what is "declaring himself down". I don't know. The only thing I know for this argument is the rule that is posted defines being down due to one of the following conditions: (a) kneeling and not making an attempt to advance the ball, or (b) falling to the ground then not making an attempt to advance the ball.
As far as "diving"? You posted the video. It is clear to see he did not "dive".. His back was to the out of bounds line and the ball was to his front. You are saying he dove backwards?
What happens, again from your own posted video, is he is facing away from out of bounds and scoops a low pass that is towards his front (and again his front is pointing away from the out of bounds). That is not a dive, period.
Btw, this is a bit of a change in your argument -- yet this one has better traction as it is now a ref's judgment call if A) he was carried out of bounds involuntarily (the momentum of catching the ball), or B) he voluntarily is going down to the ground for (what can be assumed given the game situation) to land out of bounds/cause a dead ball with clock stoppage.
Feel free to look at that video and go with A. But that is going to be a hard sell given the mechanics don't add up to say momentum involuntarily carried him almost backward of his hands meeting the ball.
To the ref's call, he is now tasked to judge either: A-the receiver was voluntarily trying to go down to the ground (for the purpose of going/being out of bounds). or B-the momentum of the catch took him to the ground.
If the ref thinks A (a reasonable assumption given the math) then the player is now required to make an attempt to advance the ball or he is down right where he first voluntarily hit the ground.
If you (and BradyFTW?) think the ref made the wrong judgment and the Bill player did not voluntarily go to the ground? Make your judgment call as you see best...