With a little legwork, its not too hard to believe.
Just another one of those little oddities of continuity that can be annoying about SWTOR.
Consider this, the Sith Empire we see in SWTOR are the remnants of the ancient Sith Empire responsible for the Great Hyperspace War. Who in turn were a product of the exiled Dark Jedi of the Second Great Schism. Its highly unlikely that the Massassai spoke basic yet the Sith of the Hyperspace War and wars to follow do. So its only logical to assume that the Dark Jedi brought their language with them, and with it the accent.
Indeed I would speculate that centuries prior to the Great Hyperspace War the majority of the galactic basic speaking galaxy spoke with a Coruscanti accent. Including the majority if not the entirety of the Jedi Order. After all the Human race originated from Coruscant and not Corellia, so the Coruscanti accent would initially be the most prevalent.
So, we can speculate that the Dark Jedi who arrived on Korriban spoke with an Coruscanti accent and spread this accent across the entirety of the Sith Empire. However two millennia passed before the Great Hyperspace War, and over that period the Corellian accent may have emerged and become prevalent, however the Coruscanti accent would have remained. Jump forward another millennia and a half and we have the majority of the Republic based galaxy speaking with a Coreillian accent and we have the descendants of the ancient Sith Empire, an Empire formed from pure Coruscanti Sith, speaking 'pure Dromund Kaas'. And so we have the English/American distinction.
I doubt BioWare thought it out in such a way, but it works nonetheless.
EDIT: Why does nobody excluding Aldeeranian nobles in the Republic seem to speak Coruscanti? Well culture changes, and over a few centuries its possible that the Coruscanti accent simply began to die out - before reemerging again during the Golden Age of the Republic. Heck one could even speculate that consequence of the Great Galactic War 'pure Dromund Kaas' speaking people integrated with society. Regardless of whether the Sith Empire win or lose I'd assume the Republic aren't going to commit mass genocide on their population.