Messi did play very well at the 2007 Copa America so he has delivered at a big tournament. In particular he was outstanding in the semi-final against Mexico and scored a stunning goal. He also had a goal wrongly disallowed for offside in the final, and was one of Argentina's better players as they were counter-attacked to death by Dunga's Brazil.
At the last world cup, despite being double marked in every game, he still created a lot of goals for Argentina, and so he didn't play that badly at all. How many goals would Higuain have scored at that tournament had it not been for Messi.
He was poor at the last Copa America though no doubt about that, as was the whole team.