[ChrisLomont]

>It only takes using an engine move once or twice to completely demolish a much better opponent in a game.

That's not true. Pick an engine, set to a few hundred points above your strength, then try to beat it using only one or two moves from an engine. You will lose nearly every game, because so many of your other moves will be so below the other player that the 1-2 good moves cannot make it up.

This is demonstrated quite often by the games where GMs are "helped" by others in multi-player games, and it shows that help against a much better opponent takes far more than 1-2 moves.

Among really close players it helps. But not once you get a few 100 ELO points apart.