I've only heard of what passes the line (in a cash game) is the bet at one casino, talk about an easy angle.
This is the worse nonsense in poker. You can find rules (written) that say if a player picks up 30 in chips, moves them past the betting line and with their hand still past the betting line, can add to the bet. They can also move chips into the pot if the first hand is posted in the pot. I'm not saying I agree with all this, but I think in the best spirit of the game. If there is a pause and the player keeps doing and say they watch someone else as they do it, you can claim an angle.
If the player picked up 40 to drop chips into the pot, and with the hand over the line puts down the 40, and says 60, the bet should be 60. There are aspects where if the next player makes an action, because the current player is too slow, it can affect the outcome.
Tournament play I would defer, but cash, the spirit of the game is action, let the action play!