As counterexample I would still call American English and Brazilian Portuguese dialects, even though they have armies and navies. I'm not sure if I would call Afrikaans a dialect.
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.
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.
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.