As you point out, most rights are balanced against other rights. The worst "right" ever written was the "pursuit of happiness." Unfortunately for us, Jefferson understood that such pursuit would be both lawful and moral. If he had been able to conceive of as perverse a society as ours growing out of the American experiment He might have phrased it differently (or retained the original).
Jefferson didn't really believe in the fallen nature of man. That's why he so fully supported the French experiment, which was a dismal failure because it did not respect G-d. Our experiment did respect G-d and has been a huge success. I say "did" not "does" and I fear the worst for the future of our experiment. If Jefferson had believed in the fallen nature of man, he might have realized that we were no less likely than Greece or Rome to confuse liberty with license, and be destroyed by it.
Shalom.