Okay, but that's not the case the assistant was making and I need to believe he's on top of the one rule that governs 90% of his job.
My interpretation of what he was saying is, "I saw Lovren make a play on the ball. Did he touch it? Because if he did it's a penalty."
There is nothing in that conversation for you to declare in your interpretation "I saw Lovren make a play on the ball".
Several times both Moss and assistant asked each other if they saw Lovren play the ball. If one of them had seen it, they could then, as you are saying, assert their observation as authority.
It looks like both referee and linesman were unsure if Lovren played the ball, and yet still used this in dispute fact against the clear evidence of Kane's offside position.