Well guys, I may be a disappointment to you on this one.
Bobby Fuller was one of my great friends when we both lived in El Paso, Texas. I played in a band called, amongst other things, The Wild Ones. Bobby went under just his own name (not The BF4 yet). On several occasions, I would play with Bobby at some of his gigs, me playing rhythm gtr and singing a song or two (especially "Oh Donna").
Bobby recorded "I Fought The Law" first at his own "home" studio, located fortuitously on Album Avenue. He had a pretty good setup for the day. This "local" version was a huge regional hit on Bobby's own Eastwood label. His parents were very supportive, as was his brother Randy, who played bass. I was around for some of this recording, but I was not a regular band member, as were the other main guys. Bobby's version was VERY similar to the eventual LA recorded one which became the national hit single.
I was not there for the LA stuff, as Bobby and I both left El Paso for the try at music business fame and fortune about the same time. Bobby had tried Nashville, without success, and was convinced California would be for him. I had heard some early Stax (then Satellite Records) releases, and wanted to head for Memphis. I had just arrived in Memphis when Bobby proudly sent me his re-recorded version of IFTL. (Wish I still had the accompanying letter!)
I too think it is a terrific sounding record; it still holds up today. I THINK there was a session player or two involved, but I'm not sure. If not, Bob there at Del-Fi probably did his "comping" trick of multiple takes on 1/4" with editing between takes. He had used this very successfully with Richie Valens on La Bamba, using the mono band track, running it through the board, line in, to mix with the live vocal mic, and making about 70-75 takes to edit amongst (RV apparently had poor rhythm).
One interesting note on Bobby Fuller: If you listen very carefully to his version of "Not Fade Away," you can hear a phone ringing in the middle solo section. That was me, calling Bobby at home, not knowing the tape was rolling! So I guess I'm playing on that one!
All the best,
Terry