More to the point, was Patrick Stewart the right choice to play a Frenchman? Was the Montreal native William Shatner the right choice to play a starship captain from Iowa? I'd say that the both establish that accents in the future don't always pin down to countries that we, in the present, understand that they come from.
To contrast, if Berengaria was a colony planet (and Vaughn wasn't born long enough after the colonys establishment for a colonial accent to necessarily develop) then it's perfectly possible that Vaughn's parents (and extended family) came from Scotland and he inherited their accent, despite classifying himself as Berengarian fr example.
Right. In the novels, I've described Jasminder Choudhury as having a "Denevan accent." In my mind I hear her as having a South Asian accent, but what's actually there in the text could mean anything, and implies an accent not quite like anything from Earth.
And as for Earth natives like Picard, the multicultural, integrated nature of 24th-century Earth society means there's no reason to assume a simple correspondence of accent to nation of origin. Heck, in high school I knew a girl who was born and raised in New England -- maybe New Hampshire, I don't quite remember -- but had a lovely, posh English accent because she was raised by an English nanny. Such thing can happen in the melting pot that is America, and 24th-century Federation-capital Earth is surely even more of a melting pot (even though it generally seems to be overwhelmingly Euro-American onscreen).