Well, technically you could say we are the ones with the accent since English was first spoken in Britain... so their way of speaking is the "native" way and everyone else has an accent.. of course they have their own "accents" within the country.. and even within the confines of London depending on what area of the city someone grew up in.
have you ever talked to someone from New York or another big city then talked to someone from Texas then to someone from New Jersey exc.? even people from different part of the USA have different 'accents' so yes (that's not even to mention people from other countrys)
i think Americans must have many kinds of accents. i have heard people from different countries speak English, their accents are very strong. Americans are from many other countries in the world, and i don't think the accents from fathers or mothers are so easy to be changed.
I had someone tell me that I had a Chicago accent. I'm from a city very close to Chicago, and the person who asked me that did not know where I was from either. I've never heard of a Chicago accent before. Have you ?
I was in New York once and got to talking to a lady that had a little girl. I heard the little girl ask her mom why I talked funny, I laughed and told her she was the one with an accent! When I first moved to Boston, I couldn't understand what they said, and until I got used to their accents had to ask them to repeat themselves over and over. I'm good with accents, but theirs defeated me for awhile. I love accents, except for when Aussies use the "up" sound at the end of every sentence, that gets on my nerves. I love Aussies, so no offense, just don't like the up talk.