I agree with the OP: Silverwood called 'play on' because he judged that the tackle wasn't complete, so if Carmont had have played the ball, that would have been a penalty against Wigan. That's different to playing advantage (for which the video ref would be appropriate). By going to the video ref to check on the tackle, what the ref is really checking for is whether his call to the player was correct. If his call was incorrect, one 'fair' thing to do could be to go back to that tackle and make Carmont play the ball, rather than giving a penalty against Carmont, as the player was acting under the control of the referee (Section 16.7 of the rulebook, if you're interested).
However, according to the rulebook (Section 16.9, below), Silverwood shouldn't have gone to the video ref for that decision at all, so the overheard earpiece comment from the video ref was the right one.
Quote The Referee judges on matters of fact and shall not subsequently alter those judgments. He may cancel any decision made if prior foul play of which he had no knowledge is reported to him by a Touch Judge.'"
The ref had a split second decision to make, and was right to go with his instincts (as the replays showed), so in the end there was no impact on the game. But it does bring up an interesting possible gap in the current rulebook. FWIW, I think that we should allow video ref help in decisions when advantage is played. (The case of Carmont's tackle wasn't advantage, though.)