I agree with that - I think it's as variable as the individual.
My mom arrived in the US at the age of 19 from the UK, and I don't remember her ever having had an English accent ( I was born before her 20th birthday) - but I think a linguist might be able to tell now, 50 years later, that she was not born in the US...she can't do an English accent to save her life though!
I've lived in the UK for over 4 years, but I'm a terrible mimic and well into adulthood (ahem!) ...I don't think my accent will ever change. With that said, I do pronounce many words differently these days, and when I hear my voice on my phone message, I'm always surprised because it sounds like a slightly different accent than the one I used to have...my DH also tells me I sound 'more American' after getting together with my American friends. But, no one in my American family has ever said I sound like my accent is changing.
As someone else mentioned, there was a time - probably a year into my new life - where I would have a problem trying to figure out which word to use when I was taking to any of my family members by phone - I really had to think about the American word. These days, I don't even think about it, whatever comes out, comes out, and no one has complained so far!