The short answer: yes and no.
The longer answer: simply does not compute. Ever since the advent of the nuclear bomb and trade largely (but not entirely) replacing warfare, a crafty illusion developed that people no longer crave revenge... well, crap shoot, nothing could be further from the truth. I see your US training and I raise you with training of nations threatened by their neighbors and by nations who fought on the Axis side for national pride and territorial gains, yet still think they were righteous to do so.
In my view, it's not the sport that's the most brutal, but people doing them. People who enter the pool, the mat, the tatami with the clear mission to destroy their rival, literally. Personally, I still think last year's UFC match between the Polish and the Chinese fighter kicking each other's faces in was the most brutal I have ever seen, and I sensed a ton of national pride and a heaping helping of racism.
Having had that mindset implanted into me for very long years, I get that level of aggressiveness.