Find me a jazz/pop/rock recording made before 1970 that can be matched to a bpm machine.
Anything with drums and a good drummer, basically. Not absolutely perfectly in time, but a constant tempo (which is more important than any given beat being perfectly in time). Example?
The entirety of Big Swing Face, for one. We can't hold everyone to the standard of Buddy Rich though, so...
Once the song actually starts at about 0:08, the tempo fluctuates around 110 ±1 bpm. At around 0:40, there's a drum fill, and after that, the song goes to about 112 ±1 bpm for the remainder of the song.
More often than not, tempo problems are a result of tension between different group members rather than a fault of any of the individually. In general, guitars and lead instruments push the tempo forward while bass and drums hold them back.
Which induces excitement in their audience, which affects the audience perception of the tempo making it seem slower, so the audience hears it as a constant tempo.
Hard to replicate that excitement on a recording and so it's noticeable to the observer, or at least to me.