“King George III agrees!”
The difference, of course, is that Lincoln was ELECTED. Unlike King George.
He was elected by a rump plurality, sort of like Bill Clinton. Elections for the Presidency should require at least a majority. With pluralities, you can elect a man that the majority hates.
Also, the right to independence would not have changed had George III been elected. It's not about how a government is constituted that matters, it is the "consent of the governed" that is the sole requirement for governmental legitimacy.
In other words you have no idea what's in the Olive Branch petition that the Continental Congress sent King George in July 1775. And most likely you've never heard of it in the first place.
Well here you go; see how many times they emphasize their loyalty to the King, versus how many times they complain that he wasn't elected: