So, a foreign prince (not the King, his brother) enrols as a student at Harvard - would he be considered a “foreign diplomat”? He wasn’t formally acting as a diplomat, and unless he happened to be officially accredited to the State Department as one, I doubt he would have technically counted as one either. Was he present in the US on a diplomatic/consular visa, or a student visa?

Also, in most countries (the US included), one’s status as a citizen/national is legally independent of whether one tries to “claim” it.