Not exactly. Lots of those little amps (5f1, 5f3, etc…) were easy to overdrive. Additionally, it’s very easy to make hot passive pick-ups. Consider one of the first, the Charlie Christian. Those things ran hot, as did some of (not all) the early esquire pickups. Things weren’t standardized back then, so others were low output. Really it’s just about wire gauge, how much you put on, and magnet strength/size.
One of the battles that was being fought back then was building amplifiers that could stay clean - “have enough headroom” - for how loud bands were starting to get. (The fender blackface/reverb amps of the 60s were originally aimed towards the clean country crowd. Fender might be linked to rock now, but was aiming towards country/western swing/jazz during many of the early years).
Additionally, you can go back a fair bit farther than this song and hear early distortion on players like Junior Barnard who played with Bob Wills. He was using earlier octo-amps that broke up in a particularly pleasing way.
