Each colony was administered by a Governor who worked for the Secretary of State for the Colonies, a cabinet member, and Member of Parliament and answerable to the House of Commons. At the time of the War for Independence only about 3% of British subjects were allowed to vote. The government of Great Britain worked on the theory of virtual representation through Parliament.
The colonies themselves were governed through the Governors Council (administrative, judicial and legislative); and the General Assembly that represented people through the governments of the towns and counties of the colony. Agents of the colonies were sent frequently to Parliment to represent the interest of the local governments and individual subjects.
The colonist were taught the interpetations of the British Constitution or the Magna Carta of Sir Edward Coke. That they had "all the rights and immunities of free and natural subjects." From his teachings the Massachusetts Assembly declared the Stamp Act "against the Magna Carta and the natural rights of Englishmen, and therefore, according to Lord Coke, null and void." Coke said "When an act of parliament is against common right or reason, or repugnant, or impossible to be performed, the common law will control it and adjudge such an act void." But regardless of whether the British Constitution actually forbade taxation without representation or merely was implied by the spirit of the Magna Carta the colonists used this "misinterpretation" to condemn the Stamp Act. In 1775 "On the eve of the Revolution, Massachusetts adopts its seal- a militia man holding a sword in one hand and Magna Carta in the other."
So in this one way American War of Independence is comparable to the Confederate War of Independence. The Colonist were fighting for their independence over the interpetation of the British Constitution (Magna Carta) as much as the Confederate people were fighting for their independence over the interpetation of the United States Constitution.