Like, you see some British guy who is actually from the Caribbean and who is really African, if you take it back far enough. Why shouldn't he be representing his home country? Should Britain claim him? Is Britain right to take that success as their own?

What about sportsmen/-women who have about 10 different races and nationalities mixed in them? Should they be disqualified?
Like me, I am Lithuanian. Doesn't mean I live in Lithuania, speak Lithuanian, or have even seen Lithuania! I affiliate myself with the USA because that's where I've grown up and it's where I call home.
Who are you to choose where you'd want to be born?
I believe they can play for whoever they want as long as they are a citizen of that country/countries. For what I believe is the first time, this year they have Independent Olympians.