I would say they are not a big three...or big four for that matter. I understand that Kobe, Nash, Howard, and Pau have all been the leaders of their team at different points in the careers but that doesn't necessarily make them a big four. They're just a complete team.
The Celtics brought in Garnett and Allen to help Paul Pierce when they each still had quite some time left in they're careers. Its also worth noting they had about the same amount of time left as well. That is the same thing that happened with the Heat. They brought in James and Bosh to join Wade.
The difference with the Lakers is they traded for Gasol years ago because they needed a big man who could shoot and play offense. He was great for their system. But that was while they still had Derek Fisher when he was still playing well. Since he left, they have needed a new point guard so they went out and signed Nash before they ever even knew if they would get Howard. They signed Howard because Andew Bynum was injured so often and played so inconsistently. Although Howard is a superstar which gives off the appearance of creating a big three or four, it makes sense for them to have someone there who can be a leader after Kobe retires. And finally, until Kobe does retire, there will be no question of who the leader is, which is the case on other teams, and this separates them from the others.