I don't think he changed his hairstyle, from memory. He just wore an alice band with it scraped back, which made it quite visible. Knowing what we do about Beckham, it's unlikely he didn't either do that knowingly, or at least do it without being concerned about the fallout, but to look at it from his perspective, why should he go out of his way to protect Fergie, given that he'd just kicked a boot in his face? He probably felt wronged.
And let's be honest, a story like this would have gotten out, alice band or not. Particularly when you consider that it has been said that Ashley Cole was in the dressing room at the time. What incentive would he have to keep it quiet?