I heard that expressed as "A language is a dialect with an army and navy"
http://en.wikipedia.org/wiki/A_language_is_a_dialect_with_an...
I found it quite true when you look at cases like Dutch vs. Afrikaans or Swedish vs Norwegian vs Danish. Declaring your dialect a "language" can be a tool of nationalism.
has army, is dialect: Schweizerdeutch, American English, Brazilian Portuguese
has army, is language: Norwegian (v. Danish)
no army, is language: Yiddish, Afrikaans
no army, is dialect: Frisian
As political power went until 1994, all heads of state and of the army (and as far as I remember, all holders of other top positions) were Afrikaners.
Nonetheless, your point still stands as I'm sure there are valid examples of 'no army, is dialect'
The way the word "accent" is used by most non-linguist English speakers, I'd say you're mostly right: People will say things like "she's got a Southern accent" – when she was born and raised in the South, speaking that same regional variant of the language that her parents spoke, ie. speaking that dialect.
It started out as a Dutch dialect or creole, of course, and it is now a separate language.
But the process formation of a separate language was political as well as linguistic.
My mother-in-law apologizes for accidentally using "slang" terms in front of my children, mostly because she was taught at school that her language was 'incorrect' and it was suppressed in favour of the 'correct' dialect of the ruling class who lived in another country.