There's an awful lot of Strat on that track. Jimmy Page did get some great clean tones from his Les Paul though, especially on live performances.
A lot of the old blues guys would plug straight into the recording desk, to keep things clean. A lot of BB King's later output on Crown Records was recorded direct. You can hear it, little to no ambience, and REALLY clean (although the desks back in those days were all tube powered). A lot of T-Bone Walkers guitar tones are from being plugged into the desk and not using an amp as well.
The first time I heard Mike Bloomfield (and knew it was him) was on a Chess album called Muddy and The Wolf. I wouldn't call the sound here through-the-board clean but I think it is within the parameters of the OP's question. And it's some good playing too:I realize that Bloomfield got some sustain from his amp, but using mainly Super and Twin reverbs, his tone was much cleaner than most of the Marshall guys. I've always considered small Fender amps 'clean' tones, compared to Marshalls and other high-gain amps. Obviously a cranked tweed Deluxe or Bassman is not a clean sound, but I think most of you understand what I mean. I'm not talking about "plugging directly into the board like Les Paul" clean, but what "most" of us refer to as a clean tone, like a Twin or a Deluxe Reverb amp.