When I studied linguistics, dialects were simply defined as regional variants of a language (and that includes the "central" dialect, which many would equate with the language itself), while an accent was what a non-native speaker would get (e.g. "English with German accent"). Whether some dialect rose to the political status of language, was a political question, and not really something for linguists to worry about until they took a course on sociology.

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.