Well, it is a fact that King George III had no actual power, it all resided with Parliament. No monarch has had any legislative power since William III & Mary II. Any laws passed from the UK onto the colonies would have come via Parliament, not the King. Allegiance to the crown is an interesting phrase, but it all boils down to the same facts; the colonists rebelled against an elected Parliament to form a new democracy, which has a similar shape (lower house, upper house, head of state). Was the motives of the Founding Fathers pure? We will never know. History is written by the victors, they say, it's not always cold hard facts. Seeing history from both sides leads to some interesting conclusions, and it's true to say that in the USA kids aren't taught about the fact the UK is a Constitutional Monarchy, with the head of state having no power. The idea of another country even having a constitution baffles some Americans - democracy and constitutions are not American inventions.
Here's another interesting fact: slavery has been illegal in England since 1066. Why? William the Conqueror didn't want the English to muscle in on France's lucrative trade in slaves, so when he took the English Crown he outlawed it in England. It's never been repealed. Hence, no slaves in England, and then the UK since 1066. Hence why I get annoyed when Americans blame the UK for slavery, sorry Oprah, the USA got it from the French, and it was part of the grievance they had with Parliament that they had to outlaw it.
The United Kingdom of Great Britain was formed at the beginning of the 18th century by the joining of the English and Scottish Crowns. Scotland actively wanted this union and signed it into law very quickly. Scotland was not conquered. Rather the opposite if you know how the royal line works, lol. (They technically conquered England, but the Scots do like to moan). Ireland? They petitioned the new UK Parliament to join the Union as well, because it looked like a good thing to them... But we all know what happened there.
Is the UK a perfect country? God no. It's a mess, like most nations. The Constitution is not one document but several that have taken shape over centuries. We've had civil wars, taken over countries we had no right to be in - and ended up with the largest empire seen on this ball of dirt. But... We have also championed good things as well.
History is always a hot mess because of interpretations. But the simple cold facts speak for themselves. History should always be viewed from the outside looking in, not the inside looking out. We should learn from it, and yes - we should let it be a warning of how not to do things. Take pride by all means, but not of the rhetoric, but of the facts.