Parody shockwave videos like the hypothetical one in question aren't the problem per se in and of themselves...but they reflect an attitude of self-importance on our part, and I think it's that attitude that causes enmity and bad feeling by people the rest of the world over.
When I was about ten my mother and I went on a trip to South Africa, then Egypt. I remember being at a bonfire at the safari camp we were at in South Africa and hearing one of the guides laughing about "Damn Yanks." I would prefer to live in the type of world where I am not hated outside of my own country, and I try to act in a way that is in accordance with that.
I mean, this is why I walked out of Team America as well - sure, there were a lot of funny bits in it, but I also took Arabic for a year at school and saw the attitude of my professor (an expatriated Palestinian) towards American foreign policy. I didn't think a bunch of puppet Arabs running around shouting "Muhammad Ali!" - basically, as I was discussing with a coworker at JAMDAT after the movie came out, more or less in blackface - is going to help America gain any respect for Arab culture. With the constant conflict and struggle in the region, I believe this is important if we as a people of the world are ever going to take a serious try at world peace. Now, I know that it's not Parker and Stone's job to be fostering international cooperation - they're in the business of making funny movies, and they're quite good at it - but I still don't have to take part in humor that I feel marginalizes people.
My apologies if I feel a little strongly about this, but I think it's well and goddamned fucked up to have one's humor at the expense of a lot of other people simply because they don't happen to live anywhere near you.