fRR, I've also been reading fanfic for years, and I maintain that usage is wrong and confusing. Insertion/wish-fulfillment is the soul of a Mary Sue.
Sometimes a character may be misinterpreted as a Mary Sue by a reader when he/she is perceived as too perfect, but when that character is nothing like the author and does not reflect the author's actual views/wishes, then that character is not a Mary Sue.
As far as I know, though, Bella is a genuine Mary Sue who reflects Stepehnie's ideal self and how she would want to react in that situation. That's the impression I've gotten, though it may be wrong.
I read a series once by Leo Frankowski, a Polish-American bachelor engineer, about a Polish-American bachelor engineer who goes back in time to 1200s Poland and jumpstarts the technology while getting tons of women to fall in love with him. The Mary Sue was strong in those books.
Fanfic in its modern form began with Star Trek, so the fanfic Mary Sue did not originate long before the term came about. However, it's true that authors used self avatars from time to time for centuries beforehand. But their usage was often more skilled due to editors not publishing crap.