Living in the USA, NBC (and affiliated networks) has hosted Olympic coverage since I can remember (I think it was CBS at the 1998 Winter Olympics in Nagano).
Why does NBC host Olympic coverage in the USA?
Because they paid the most for the rights to show the Olympics.
proof? from the June 7, 2011 LA Times:
NBC holds on to Olympics through 2020 with $4.3-billion bid June 7, 2011 | 12:20 pm
It is rare that the incumbent is the underdog, but that's what NBC was when it came to holding on to the U.S. television rights for the Olympics.
With rivals Walt Disney Co., owner of ESPN and ABC, and News Corp., parent of Fox, expected to make aggressive bids for future games and the body language of NBC's new owner, Comcast Corp., indicating a wariness of big-ticket sports events that bleed red ink, the peacock network seemed to be far from a sure thing to remain the home of the Olympic flame.
But when the smoke cleared in Lausanne, Switzerland, it was NBC that walked away with the rights to the Olympics through 2020. The price tag for the four games is $4.38 billion. The breakdown is as follows: The 2014 Winter Games in Sochi, Russia, will cost $775 million. The 2016 Summer Games in Rio de Janeiro will cost $1.2 billion. The 2018 Games will run $863 million, and the 2020 Games will cost $1.4 billion. The locales for the 2018 and 2020 games have not been determined yet.
Comcast Chief Executive Brian Roberts, who traveled to Lausanne with the NBC team for the presentation and bid, said, "I absolutely wanted to win for the team."