I've seen that video a few times. It is definitely not a fake, as I also saw a follow-up interview with the medic depicted there. IIRC, it was a 7.62x54R, and shattered his SAPI plate, bruising his chest. The medic can't complain, the plate did exactly what it was designed to do, and he suffered no ill effects other than a wicked bruise. He was definitely not shot with a .50 caliber weapon system though. No body armour that I am familiar with can stand up to that kind of trauma.
A .50caliber or 12.7mm rifle in the hands of the insurgents was not all that uncommon. During the buildup for Operation Al Fajar, Muslim fighters from the world over came into Iraq to take a crack at the Infidel invaders. A significant amount of Chechens were encountered, notable because they were the best trained and armed. They had been fighting the Russians for years, and had aquired some interesting bits of weaponry. Remember,the Americans are not the only military to field a rifle of that caliber, the Russians used them too, and reportedly some Chechens had them, and used them with marginal success.
The tungsten bullet bit is odd, RCmodel being correct in that a solid tungsten bullet would strip a barrel of its rifling, yet I've been around enough to trust the guy on the ground, and if Essayons21 says that it was pure tungsten and had rifling marks, then it did. Hard to say what its intended purpose was, or how it was fired. The insurgency is constantly improvising and adapting, and they recieve help from outside the country as well (EFP's from Iran, for example) so it is difficult to say with any certainty what that is all about.