What law prevents the arriving player from using his hands to hold or push the gathering player from getting to his feet? I do not know. I cannot find a law that gives the gathering player the right to stand up.
14.1 PLAYERS ON THE GROUND
(a) A player with the ball must immediately do one of three things:
•
Get up with the ball
• Pass the ball
• Release the ball.
Sanction: Penalty kick
(b) A player who passes or releases the ball must also get up or move away from it at once.
Sanction: Penalty kick
(c) A player without the ball must not lie on, over, or near the ball to prevent opponents getting possession of it.
Sanction: Penalty kick
(d) A player on the ground must not tackle or attempt to tackle an opponent.
Sanction: Penalty kick
14.2 PLAYERS ON THEIR FEET
(a)
Falling over the player on the ground with the ball. A player must not intentionally fall
on or over a player with the ball who is lying on the ground.
Sanction: Penalty kick
(b)
Falling over players lying on the ground near the ball. A player must not intentionally fall on or over players lying on the ground with the ball between them or near them.
Sanction: Penalty kick
The bit I've underlined tells you they can stand up. However, if before he's done that an arriving player has contested the ball. the man on his feet is king.
The man on his feet is not explicitly told not the play the man. However, the inference of the quoted law 14.2 suggests that he is not to "kill" the ball. Therefore, allowing him to rip the ball but not hold it in to the player on the ground is logical.