I suspect he probably grew up surrounded by it. I knew many "red diaper" babies (I grew up in NYC and went to a very liberal public high school) and they had grown up listening to the Internationale and various Depression era protest songs (such as those written by Arlo's father, Woody Guthrie.) I'm sure Arlo Guthrie was one of Daddy Berg's favorites, so no doubt his kids heard the song and others like it a lot.
It tells us something about the atmosphere in the house where Nicholas Berg grew up, at least.
Nick Berg has a lot in common with the Portland lawyer, Brandon Mayfield, who was arrested Saturday after a fingerprint found in a shopping bag of detonators in Madrid following the bombing attack was identified as his.
His family is leftist and opposes the war and GW Bush, and his brother has been outspoken about it.