Not necessarily. Sure, I think the US is the best country in the world... for me, anyway. Everyone is free to think their country is the best in the world for them, move to whatever country they think is best, or try to make their country better, and I wouldn't blame anyone for it. (In fact, I think it's great.) This comes with the freedom to form our own opinions and make our own choices. Though I do get annoyed with people who live in one country (whatever it is) and enjoy all the benefits of citizenship, but do nothing but trash talk the whole place and all the people.
Furthermore, here we have a lot of people whose ancestors didn't come here of their own free will. It's kind of hard for me, for example, to find any ancestor of mine who didn't come here as slaves - I mean, "permanent indentured servants," under threat of starving to death, or just "disappearing" after expressing dissatisfaction with the regime (the German side).
Also, people have the right to define themselves however they wish provided it's honest and does no harm, and keep whatever traditions they want. Also, demanding someone renounce their roots, their traditions, or their identity as a quarter this, a quarter that, and half everything else, just because they don't live in the country or countries of their ancestors strikes me as, well...
... a bit too similar to the mentality that made my grandfather's processing at Ellis Island a traumatic event he didn't care to remember (this after he fled Nazi Germany with just the clothes on his back), and the long term consequences that even I faced of his refusal to Anglicize his name.
There's also a more horrific reason behind our obsession with minute fractions in our ancestry. Even to this day, recognition of treaty rights for Native Americans can depend on these fractions.