An easy way to understand what a NBC is, is if you take away every law created by the government granting citizenship, the 14th Amendment, the Immigration and Naturalization Act, every piece of positive law - and you would still be a US citizen, then you are citizen by natural law, ergo an NBC.
A very good way of putting it.
When [my wife] became a US citizen, she was told that the US does not recognize her other citizenships.
And, when you stop and think about it, why should we? Frankly, I'm not aware of any nation which recognizes and considers the citizenship laws of other nations to take precedence over its own. It's simply not in any country's interests to let another country write its citizenship laws.
Dual citizenship for American citizens becomes an issue only when it leaves them subject to the laws of another country -- while they are present in that country. For example, during the sixties and seventies, many children born as American citizens overseas found themselves subject to the draft in the country where they had been born. Consequently, it was important to avoid visiting that country -- where they could be held subject to its laws.
That is of course applicable if the IDENTITY of the indvidual claiming citizenship is known. In this particular instance, what you have is a CLAIMED identity, so I imagine the citizenship question is moot.