The point of the JFK link you cited seems to be that both of his parents' families were from Ireland. That's not the case with Obama; his parents and their families are from different countries. And it's one thing to claim someone as a descendent of your country, but there are people in Kenya who said Obama was born there. Who has ever said this about JFK with Ireland???
If they said he was born there it’s different (not that them saying, makes it so) but claiming heroes, famous people, feta cheese, salads or Turkish delights for your country is an old trick. The Balkans are a prime example of it :)
In most of the world, by custom, you are what your father is.