My daughters were born on English soil while I was stationed in London, and they most certainly have dual citizenship. To say you are not subject to the jurisprudence of a foreign country would mean that you could not be locked up for breaking their rules. Americans overseas are locked up every day! In reality, only diplomats can break rules and not be arrested.
The rub for me (and my daughters) is that since they have dual citizenship, they are not Natural Born Citizens of America, therefore can never run for the office of President. Bummer.
As a British anchor baby, my father was in the Air Force, I was consistently told growing up that as a dual citizen, I could never run for president.