Things aren't so simple, because football is a sport where we should play the ball and not the player, but in which contacts are still tolerated. As such it's relatively easy for players to hit their opponents, as long as they pretend to play the ball.
What needs to be understood is that football is played with very fragile parts of the human body: ankles and knees. As such, dangerous play isn't really about Zidane-like headbutting... that's impressive, stupid and against the spirit of the game, but it's not really dangerous or "dirty".
Dirty play is more like pretending we play the ball, but constantly targetting opponents knees and ankles, that's how you "destroy" a player. And when you watch Iniesta's knees in the airplane after the final (in the youtube video previously posted in this thread), you clearly see that Dutch players have hit hard, and on purpose. That's clearly dirty play, no matter the side of the pond in which one lives in.
Actually, the laws of the game make it quite easy to stop the dirty play: you just need to send off a player and that generally calms down everyone.
The issue in here was that it was the world cup final, the most important match out of 4 years on the planet, all sports combined. The referee didn't want to ruin the game in reducing the Dutch team to 10 players after 20 minutes of game. Dutch players understood it rather quickly and didn't hesitate to abuse from the situation.
If many people considers the game was badly refereed, it's not really because of any specific bad calls, it's mostly because the referee didn't succeed to control the game as he should have, because he was too lenient during the first 70 minutes.