The one drop has been official US practice since its founding. The first census ever performed in the US required counting blacks even down to the precise percentage of black 'blood' (i.e. quadroon, octoroon, etc). The one drop rule is also the accepted standard when determining if a person is a given minority for the use of certain government programs, etc. For Native American counting the smallest accepted standard is 1/16th. Initially a social practice, it was later codified in some states in the post-Civil War and early 1900s during the Jim Crow era in the southern United States. "Tennessee adopted such a "one-drop" statute in 1910, and Louisiana soon followed. Then Texas and Arkansas in 1911, Mississippi in 1917, North Carolina in 1923, Virginia in 1924, Alabama and Georgia in 1927, and Oklahoma in 1931. During this same period, Florida, Indiana, Kentucky, Maryland, Missouri, Nebraska, North Dakota, and Utah retained their old "blood fraction" statutes de jure, but amended these fractions (one-sixteenth, one-thirtysecond) to be equivalent to one-drop de facto."
With regard to the girl in the video, the issue of 'passing' is not applicable because she lives in an era in which there are no official sanctions for being black that she is trying to avoid by 'pretending' to be fully white. That is what 'passing' is: the deliberate attempt to deceive the dominant white majority into believing that you too are fully white in an attempt to take advantage of opportunities and advantages not allowed to non-whites. She is not denying her black parent or hiding, she is simply making a decision based on observable physical appearances, not attempting to assert that she is one race over the other. Perfectly understandable.
And with regard to how I choose to see myself, I make a decision based on the contemporary circumstances in which I find myself, and those circumstances are as a person of African descent, universally viewed as such, with a variety of inputs into my racial and ethnic makeup, only 1 of which is socially or politically relevant. Where I in a dark-skinned environment, populated solely by full-blooded black Africans this would not be the case. But since I am a black minority member of a white majority society founded on white American-style racism, that is the most relevant aspect of my reality. Were I to be the suspect of a police manhunt, the APB would state my race as black. In school I am categorized as black and in the job market I am treated as black. Claiming to be white and touting my white ancestry would get me bounced out of any job interview as either schizophrenic or an idiot, regardless of how many whites may grace my family tree. People are quite free to have whatever world view they choose. I have a unique one as well. But willful ignorance of the reality in which one finds oneself and the world view largely shared by the majority of US society (and by extension to a greater or lesser extent as a byproduct of US cultural/economic/military hegemony, the world) is not wise, healthy or safe.
The facts of the origin of non-African blacks are the facts, whether I like them or not. Claiming that I am a white Englishman or a white Spaniard because of a variety of chattel slavery relationships in my family history does not make it so. I am quite happy with myself and the lack of historical continuity within my family history doesn't bother me much because I had nothing to do with the injustices, however horrible they may be, done to my ancestors. But they are a fact of my existence, period, and I do not lose any sleep agonizing over them.