Yeah, I really don't have a problem with that characterization.
When in the Course of human events, it becomes necessary for one people to dissolve the political bands which have connected them with another, and to assume among the powers of the earth, the separate and equal station to which the Laws of Nature and of Nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.
That is exactly what it is
The next-to-last paragraph of the Declaration speaks of our “common Kindred” with the British, and our “Consanguinity.” That is a watered-down version—Jefferson’s original draft was longer and more emotional about the break-up.