Right, those Englishmen by birth, only called themselves Americans after they justified their rebellion -using their rights as Englishmen-. That was the point of the Declaration of Independence, and it follows that very pattern. It begins with them identifying themselves as loyal subjects who deserved full rights, then lays out the "long train of abuses," the legal justification for treason against the Crown as their final and only option of redress to secure for themselves the same rights that were being infringed. Not any "new" rights, the same rights. Only after that justification is made do they refer to themselves as a separate entity from Britain, while the British never considered them as anything other than Englishmen (but chose not to hang those they caught as traitors).