This is an imperfect analogy (since there is not really a concept of "citizenship" for individual US states), but note that claiming residency in one state while living in another will often require you to pay taxes in both.
> Nobody else (worldwide) does this. It doesn't make any sense.
I think it is pretty clear its purpose is to prevent US citizens from deciding to live abroad in order to pay less income tax. The legislation that requires US citizens to report foreign bank accounts (which some of the people in the BBC article mention) is called the "Foreign Account Tax Compliance Act" [1] is supposed to prevent all citizens from committing tax evasion by hiding funds in foreign bank accounts.
I think there are multiple reasons why you or others could argue that these rules are counterproductive [2] or otherwise detrimental to the interests of the United States, but I do not think they can be dismissed out of hand.
[1]: http://www.irs.gov/Businesses/Corporations/Foreign-Account-T...
[2]: https://en.wikipedia.org/wiki/Foreign_Account_Tax_Compliance...