Tami, you are so right in that it seems to be society, and in particular whites, who confer racial identity upon people, precisely as White America perceives you. The operative point though is that the one drop rule comes into play because, as soon as they have "proof" that the person has Black blood, they will be "re-classified" as Black. The crystallizing event for me occurred in college. I was assisting a student in the computer center of the college. When she left, a white professor, who was talking with another administrator actually asked me, "is she white or black". I was first shocked but immediately answered that she was black. In other words they were looking for confirmation, despite her appearance. That could have taken place if they had seen her father or mother, both of whom were Black, or it could come from an external source, like my confirming her race. In either case it would satisfy the "one drop" rule and the person would be considered Black.
Obviously, you know about this history in the states, and even the categories that were created so that whites would know the racial identity of Blacks, and not just consider their appearance. Mulattoes, 1/2 Black blood, quadroons, 1/4 Black blood and octroons, 1/8 Black blood. So, indeed there are Americans who would consider the marriage of a 1/4 Black man and a white woman as an interracial marriage.