Having just read all of this, there is a fair bit of patriotic sniping going on here...
First up, for me, is this. If you want to know why people are ashamed of activities of others, it's because of this - people are ashamed that THEIR culture can produce anything that is as bad as whatever it is they're ashamed of. For example, take Germany. 30 years ago, if you tried to get anything about Hitler and Nazi Germany out of a German, you would find they are ashamed of it, even if they didn't have a part in it.
True, admittedly some of the population of Germany were at the time from the same generation of people who had served under Hitler, but all the same, it's the culture shock thing which affects people - when your way of living, your entire social policy is revealed to have flaws and when you consider your country to be at a height of it's power/history, you start to realise you can't believe you supported it. That's why people are ashamed of their countries past - some of the things that have happened before are NOT excusable, and realising that contributes towards progress of social policy - you can avoid the mistakes people have made before.
Second of all - there is absolutely no way in any shade of hell that the UK would remotely entertain being a State of the US. Believe me, you might have your declaration of independence, but as was said before, that would restrict both your country, and the UK itself would most definately disagree with it.
Fact is, if the UK was a member state of the US, how many priveledges would it have to give up? Do you think the entire population of the UK would want to sit and wait for Congress to argue whether or not a small socialist island should get it's rights? For me, I feel we'd be treated effectively like a colony. A distant branch not worth thinking about, and for one of the world's previous empires, to be regulated to a backwater US 'colony'... I don't think that is remotely likely to happen. Self-determination would play a big role. As was said, America would have hardly been likely to listen to British rulings anytime soon, but the inverse would run just as true - the British would be unlikely to listen to American rulings anytime soon, and would be quite possibly the most defiant state you ever adopted.
Also, on this topic - colonisation does not mean forced invasion and taking over. India was taken over by the British without so much as killing any leaders or mass slaughter of people, yet was a British colony. Working your way into the ruling system and taking over that way still counts as a colony.
Ultimately... I'm proud to be British, and I don't pretend I'm not. I realise, however, exactly the reason why America and Britain are different. I don't hate America, but both the British and Americans live different lifestyles - we do things our way, you do things your way. I would say, to a degree, Britain is pretty isolationist in terms of the population's viewpoint. They seem to want to be left out of things for now, and after two world wars, a few middle-east wars... who can blame them? We fight our wars in modern times to defend our own freedoms and the freedom of others at times. (Sounds a bit patriotic... can't really think up a better phrasing for it)
Some of the things the British have done are inexcusable. Even though I was not a part of them, I wouldn't want to see them happen again. Slavery is just one of the things.
A side question here is this... How would a member state of the US go about actually LEAVING the United States? Last time that happened, a fair few people got shot dead for it. As far as freedom goes... what happened to freedom to leave the United States? For the ultimate democracy to not allow that does question the title of 'democracy', as only empires practise subjugation of territories under it's control.