Is it right for Athletes who live and work in the US to represent other Countries at the Olympics?

To me this seems a little mercenary, Athletes for Hire, if you will. I thought the Olympics are supposed to be a venue where the worlds best ameture athletes can gather and compete representing their individual nations. If an athlete has spent the majority of their life living and training in one country, I feel they should represent that country. Not a country they happen to be born in. What do you think?