Wait. This response doesn't make sense.
In the USA the vast majority of folks who are at least "half black" will automatically get put into the black category. A 255 person? Maybe not. But a 50%? That's almost a lock. Yes, there have been recently more questioning of this by white folk who, perhaps in fear of their shrinking numbers, are now wondering why a child from a black parent and a white parent is often considered "black". Tough luck to them since for like 200 years in this country their ancestors, great grandparents, grandparents and parents clearly put such people in the black box. Those old habits are hard to break. A guy like Obama would have been labeled black in almost every part of America so I don't see where you're coming from. Its not as if he could "pass" like that dude from Prison Break.
And the one-drop rule meant, sir, one was automatically considered black even with the smallest fraction of black/African ancestry. So maybe you worded that part wrong because CLEARLY ARod and Obama would qualify.
In Latin America he is not necessarily black because in latin America they are not as quick to use racial dscriptions like that. In latin America ARod would first be identified as Dominican.
The "culturally black" argument we can agree on. But let me point out that "black" is most often used to refer to African Americans or the black diaspora living in western nations. In Africa the term "black" is not used as much as it in the USA (relatively speaking). And nor should it be. It would be mostly unnecessary anyway. There are people in Sub Sahara Africa who view themselves as African but view black people in America as "black" and that too has more to do with cultural differences. The "black" definition/description/category isn't perfect but neither is "white".