My belief is that people point out nationalities of birth for different reasons, some more problematic than others. For instance, on the way up to his gold medal in Seoul, Ben Johnson was only ever referred to in the Canadian press as "Canadian sprinter Ben Johnson." After he tested positive and lost his medal, you could easily find articles in which he was referred to as "Jamaican-Canadian Ben Johnson." There's an excellent discussion of this here: "Exorcizing the ghost: Donovan Bailey, Ben Johnson and the politics of Canadian identity." Steven J. Jackson in Media, Culture & Society © 2004 SAGE Publications (London, Thousand Oaks and New Delhi), Vol. 26(1): 121–141. It wasn't necessarily racist; it was, however, an attempt to "un"-Canadian him after the scandal, even though he had lived in Toronto since he had been 15 and had developed as a sprinter (and as a steroid user) as a thoroughly Canadian athlete. So yes, sometimes identifying another country of birth and making someone a hyphenated American is an innocent attempt to provide additional context. But sometimes it seems an attempt by people to undermine the athlete's claims to citizenship or their rights as a citizen by implying that they're somehow not "real" Americans. Many people believe that this happens more often for athletes of colour than white athletes.
I think I know why it drives people nuts when we point out where people are born. I think it's because most runners like to think they are good at running as they are hard workers. The beauty of the sport is the harder you work, the better you get (normally). But statements like Kenyan born remind people there is a HUGE GENETIC and ENVIRONMENTAL aspect to it that has nothing to do with hard work.
People don't want to admit that so they attack the messenger.