I came across some random article on this a few months ago.
It seems this "false" accent was actually taught to actors in the 1930s & 40s, and started in New England boarding schools back then to pretend people who could afford to go to those schools were somehow better than, well, people.
I can't find the article I read but here's a discription from wikipedia I found:
The Mid-Atlantic accent, or Transatlantic accent, is a consciously learned accent of English, fashionably used by the late 19th-century and early 20th-century American upper class and entertainment industry, which blended together features regarded as the most prestigious from both American and British English (specifically Received Pronunciation). It is not a native or regional accent; rather, according to voice and drama professor Dudley Knight, "its earliest advocates bragged that its chief quality was that no Americans actually spoke it unless educated to do so". The accent was embraced in private independent preparatory schools, especially by members of the American Northeastern upper class, as well as in schools for film and stage acting, with its overall use sharply declining after the Second World War. A similar accent that resulted from different historical processes, Canadian dainty, was also known in Canada, existing for a century before waning in the 1950s. More recently, the term "mid-Atlantic accent" can also refer to any accent with a perceived mixture of American and British characteristics.
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