Interesting. Everyone goes with the referees call for a Red lineout even though this creates a turnover in reds favor.
Nobody would go for "My error, not in touch, we'll restart with a White scrum in 15"? That seems the most equitable for the players.
But how do you know it's your error? Someone without any standing in the game told you so. This is the thin end of a very dangerous wedge. At the next penalty, the same TJ alerts you to the fact that you missed the fact that the tackler was not in fact 10m back when the ball was tapped - do you acknowledge your error and advance the penalty? If not .... then why the inconsistency? The law is clear:
[LAWS]6.A.4 (a) The referee is the
sole judge of fact and of Law during a match. The referee must apply fairly all the Laws of the Game in every match.[/LAWS]
[LAWS]6.A.6 REFEREE ALTERING A DECISION
The referee may alter a decision when a touch judge has raised the flag to signal touch.
The referee may alter a decision when an assistant referee has raised the flag to signal touch or an act of foul play.
6.A.7 REFEREE CONSULTING WITH OTHERS
(a) The referee may consult with
assistant referees about matters relating to their duties, the Law relating to foul play or timekeeping and may request assistance related to other aspects of the referee’s duties including the adjudication of offside.[/LAWS]
If you trust the TJ (and I was a non-vested coach of another team) then go to the White scrum because a. it's the fairest call and b. the players know you got it wrong.
Insisting that you're right when you err puts you in a worse light than admitting you made a mistake. Referees aren't expected to be infallible but they are expected to be fair.
If your decision was obviously incorrect, this may be the correct call. But for something like a foot in touch, very few if any will be certain about the facts and the rest will perceive you as influenced by irrelevant external factors. You lose credibility, which you are unlikely to recover during a single match. There is no reason not to admit the mistake if you are certain you made one but it was not obvious to all; but you still start with the lineout which was awarded by the sole judge of fact and law before external influences made him doubt his judgement.