When you look at leadership you don't look at what the player does, you look at the effect he has. Did the team remain calm? Did the team play out the game? Did the team ignore the poor refereeing and concentrate on a game they had in their hands? No. If Beckham was the leader in this situation, it goes down as an epic fail. Next leader please!
It's a very unique talent, to be able to fire the team up when it needs it, press when the team needs it, stay cool under pressure when the team needs it, etc. You're absolutely right, a good leader on the field will influence the players around him to do likewise. Beckham can be a great motivator and can inspire others, but he is too much at the mercy of his emotions to truly lead the team consistently. I think he's at his best when he plays alongside a strong captain.
That being said, I liked the way he played. I'd rather have him hustling, playing defense, and getting in other player's face. Natalie says he looks like a thug right now but I dig it.