Delta was in fact the official airline of the 2002 Winter Olympic games in Salt Lake City. SLC is Delta's western hub and as such, Delta was the prefered carrier for transporting athletes and spectators to the games. Delta's sponsorship can be easily seen with its massive Olympic-themed pamphlets, etc as well as the 777, 757 and several CRJs painted with special SLCWOG livery.
I question why you would think that United was the official airline.
Ignorantia juris neminem excusat.