"As to US English sounding more original, I've seen a lot of debate on this. Some say particular UK accents are closer to Old English and the US is closer to Modern English (16th century), whereas others claim the idea is simply part of American mythology."
The whole argument doesn't make sense, the view is that American English never really evolved much but British English changed a lot, yet the problem with such theories is they don't explain why American English is magically the one that didn't change. What about Australian, Canadian, New Zealand, South African English and so on? They diverged in their own ways.
But there's another more fundamental reason why it's stupid, there is no such thing as "British English" by way of the spoken word and there never has been, Scottish, Welsh, Irish, but even in England itself, Liverpudlian, Bristolian, Geordie, Cockney accents are all as different from each other as most American accents are from Queen's English and it's not just accents but local words and terms too. A bread roll in Bristol is a bun in Yorkshire, but a bun in Bristol is normally something sweeter and glazed.
Ultimately the idea that American English is some pure form of English with the closest historic ties is just stupid, America is a country born of mass immigration and if anyone seriously believes that the earlier English accents were retained in the face of mass immigration from countries like Germany and Ireland then they're having a laugh. It's not like British English immigrants were anything other than a minority of the population in the face of many other immigrants all with different accents and languages ultimately distorting the English that was originally taken across.
This also explains why Australia, New Zealand, Canada, South Africa and so forth didn't retain the same supposed classic English accent either, because accents were all ultimately immigration driven - South Africa's English accent being influenced by the dutch for example.
But ultimately the country least effected by immigration forces on accent is still going to be England, yet even there it depends where. London has seen far more immigration over the centuries and seen it's accents change as such as a result than somewhere like Cornwall, or Scotland where classic accents are retained much more closely.
So yes if you compare some American accents from areas of America that retained the heaviest balance of early English immigrants against somewhere like London that's been hammered by immigration from every area of the globe you may indeed find that their accent is closer. But if you compare even those places to somewhere like Scotland or Cornwall then you'll be a lot further off any old English accents than Scotland/Cornwall are off their old British accents.