In folk dialectology — the dialectology of ordinary people (not professionals) — some people are perceived as “having an accent”, while others don’t. Many times, but far from always, the people reporting on these phenomena believe they are accentless; accents are something other people have. (Typical folk reflections on these matters, in a California context, are noted here.)
And so we get, from Kathryn Campbell-Kibler (a card-carrying sociolinguist) this morning on Facebook:
Datum of the day: “Im sick of being told i have an accent. Bitch im from cleveland, you have the accent”
KCat is working this into a conference abstract on accent perceptions.