Your analogy does not work. People can accept the Pope as the head of the RCC and admit that he is the legitimate head of that denomination. However, at the same time, they can also belong to a denomination that does not accept the Pope as its head. Orthodoxy, for example.
Similarly, people can recognize that GWB is the legitimate President of the USA while, at the same time, living in a country that does not recognize him as their head of state. The United Kingdom, for example.
That's exactly what Lee said about Lincoln in the mid-1800's.