So, there's some truth to this, but not in the way that you've summed it up.

Crucially, you need to understand that there isn't a "the English accent". It's also important to remember that as wildly different as accents in England are now, they were even more different from each other several hundred years ago.

So which accents are we talking about for this story? Well, the early American colonies had settlers mostly from London and Southern England.

This is the accent that then diverged.

At the time, and in the South of England particularly, speech was becoming less rhotic. In the American colonies, however, it retained its rhoticity, as it still does in many parts of Britain even today.

This is further complicated by the fact that later massive influxes of people came from parts of Britain that did retain rhoticity in their accents, in particular the West Country, Scotland and Ireland (incidentally, all which still have it today).

So, like I said, there's some truth to it, but it's not quite as you've phrased it. Elizabethan Brits didn't sound like modern-day Boston folk. Americans very much have accents all of their own, influenced by not just by native English, but speakers of other languages too.

So, it's definitely a neat little tidbit, but it's usually wildly mistated!

Oh shit apparently this is kinda a thing