No, in one of the scenarios players are fighting over the ownership of a ball. As far as the players are concerned they HAVE identified their ball. The committee MAY be able to resolve the dispute......determine if one player actually has identified their ball. See Rulesman's post above. If not, then yes the ruling would be 2 lost balls.
In the other example, because there was no disagreement, there was nothing for the committee to decide. Neither player knew which ball was his.
It gets too complicated when we have two discussions going on at once in the same thread.
The original situation from the first post had only one ball in question, but with 2 players claiming ownership. For Player A, it was only an abandoned provisional ball, so it wouldn't even affect his score. That player was virtually certain that the fellow competitor's ball hit a tree in the fairway and would be found well back of where the the dispute was taking place. Player B refused to even consider that or to look for another ball. Player A also had evidence of a consistency of putting his identifying mark on his balls because he had several others to in his bag for proof. Player B did not offer any such evidence, only his word. The mark in question was not just a simple dot as is commonly used, but was a large red splotch which it is unlikely that two random players would both use. If I was adjudicating this dispute, I'd have strongly suggested that we all go back and search for Player B's ball where Player A said it should be. Any further ruling would be delayed until that was done.
This is more straightforward, with 2 players and 2 balls, both marked the same, and neither player able to prove which is which. The rules are very clear on this the baoth ball are lost and both players return to the previous spot under stroke and distance.