Well, the Colonies fighting against the Crown were engaging in an act of treason, and saying they were not part of the Crown did not change anything until they actually left the British empire.
That's true. It was taking a huge chance, on not much more than the conviction they were right. All they had to support them was some political theory of John Locke and the French philosophers, and a general and growing bias toward reason as a general principle.
They were really out there.