You are getting confused. Something incorrect in law doesn't involve a matter of opinion decision, it involves a factual situation. So for example, the referee cautions the same player twice but doesn't send the player off is incorrect in law. Messing up a penalty kick as Keith Stroud did recently is incorrect in law. Starting play when one team has 12 players on the field of play is incorrect in law. And so on.
Over-ruling an assistant on offside isn't incorrect in law, it is a decision in the opinion of the referee. As a neutral assistant if the referee waves you down you put the flag down and get on with it, even more so as a CAR as at the end of the day you are there as a member of one of the participating teams, not as part of the officiating team.
I had it happen to me, I was CAR for my team and I was a L3 referee at the time. I hadn't told the referee that, but he probably knew given that I had appointed him to the game and we had also worked together on games previously. He waved me down on an offside, I might have been a little miffed as I knew I was right, but you have to accept that the referee is charge. For that matter I got waved down for an offside in a Conference South game, again I knew I was right but you just have to get on with it. After the game the assessor confirmed that the offside decision was correct, but also that I did the right thing in dropping the flag and getting back into position once overruled. The referee lost marks as the decision was incorrect, and as the assessor said, "you've hung your assistant out to dry".
