I disagree. Not every Bostonian's accent is a Boston accent. Plenty of Bostonians are immigrants, for instance. Then there are second and third generation accents -- Jimmy Tingle had a great bit where he does an Italian immigrant accent, then a first-generation Italian accent, then a second-generation Italian accent.

They are, of course all accents of Bostonians, but I wouldn't call them Boston accents exactly.

Well, the second-generation Italian one is a Boston accent, because it's particular to Boston, but the first-generation one is more universal.