I had the impression it was about one of those Rosie the Riveter types who worked in the factories during World War 2, but the Sedgwick angle is interesting, too. I dig the 'earthy' simplicity of this tune - there's not a bad tune on "Beggars"!
It's true, Mick Jagger and Edie Sedgwick tied a friendship, they both adored each other. The song Factory Girl indeed doesn't refer to Edie. Mick dedicated much later a song for Edie, namely Like A Rolling Stone (Stripped, released in 1995 during the Voodoo Lounge tour). Originally a Dylan composition, Bob wrote this ballad especially for Edie Sedgwick.
not sure if a pulp fiction reference but "I don't need you to tell me how fucking good this music is, okay? I'm the one who listens to it. I know how good it is. When Bonnie listens to music she listens to shit. I listen to the gourmet Rolling Stones stuff because when I listen to music I wanna feel it. But you know what's on my mind right now? It ain't the music in my record player…" lol I'll stop there