Why can't you be 1/3 a nationality?

In the hypothetical case of someone with three grandparents (i.e. someone whose parents are half-siblings) that person could make a case for being one-third something - not by genes but by grandparental influence.

An interesting hypothetical, but it still doesn’t work to produce thirds, I don’t think. Assuming the same grandfather with two separate grandmothers, the grandfather’s contribution is still half, with each grandmother contributing one-fourth each.

Please explain the way the other “three grandparents” thing could work.

“Other countries (such as the US in recent years) may treat their own naturalization oaths’ renunciatory language as essentially meaningless and take no steps to enforce it at all.”

From here, middle of the page.