Perhaps regarding CX, but certainly MTB, which was my initial point. But not only that it was invented in the US, but precisely when in the late 70s. This was when families started to invest in outdoor recreational activities, and the idea of "fitness" and weight loss became part of popular American culture (diet soft drinks, light beer, those ridiculous morning exercise shows with that tan guy with the frizzy hair and short workout shorts, etc.) And, of course, families had the disposable income to buy equipment. Skiing as a truly popular family activity, to cite another case, began to really take off at this time. The MTB arriving on the scene then, with its pioneering, outdoorsy and grass roots appeal and without a Euro patrimony, but that "Made in the USofA" mark, puerile as this may be, played right into popular American patriotic sensibilities. Moreover, that California (and Colorado, where the USOC is located) was the locus where MTB first took off in the 80s, from the business and marketing perspective, the nascent activity/sport could not have had a more auspicious beginning.
That MTB further created a US branded off-road alternative to road cycling, and again became popular early in the state where USOC has its headquarters, made the sport's Olympic debut at Atlanta in 96 almost a foregone conclusion to its natural marketability, I think. One could even recall that US global influence was at its peak then, in the wake of "end" of the Cold War and the implosion of the Soviet Union, as another possible contributing factor as to why America got it's homegrown sport, which wasn't that popular elsewhere, an Olympic birth at this time. The rivalry between the two superpowers had, after all, marked the Olympics for the past four decades (remember the 1980 and 1984 boycotts by Washington and Moscow respectively). And then with Atlanta 96, as Logic pointed out, MTB took off from there internationally.