Some of the early AC motors that were driving the capstan used the incoming mains frequency as a reference.  I had a turntable in the 70's that was locked to the mains frequency. In Canberra where I lived the mains frequency was incredibly accurate. (Snowy Mountains Hydro setup is what Canberra uses. Some Hi Fi enthusiasts had a mains frequency digital readout!)

But in the areas where some of those early machines were used the incoming frequency may have been unstable. And voltage too. Now, a modern capstan motor gets its control from an independant circuit that is not involved with the incoming frequency of the mains. So we are playing the tapes on much more correct and stable capstan drive control. Even over a relative short time the recording speed may have drifted up and down on those early sessions. So obviously if the playback speed is very accurate, we are going to hear the recording variations as pitch tuning movements.

Using pitch is a good way to tune each section so they agree. I am lucky because I still have a massaive analog tape library including many multitracks as well as stereo masters that have yet to be transferred. They have all been made on modern accruate capstan drive control motors.

It is still nice to varispeed a multitrack session up/or down in speed and track new parts in the higher/lower tunings. When it is played back normally, the instrument takes on new sound qualities. Due to our fundementals and harmonics all moving around a little too. It is especially interesting whe you double or half the multitrack speed and track new stuff. (mandolin played down an octave sounds amazing. I think Hendrix did a bit of this)

True and accurate varispeeding would be a great feature in a DAW of course. And varispeed that can be automated and that automation recorded. This should speed up (Sorry ) the process of doing exactly what this engineer was referring to and that is corrceting for recording speed variations.

I am curious whay they did not pitch it all down to A = 440Hz. Is it because the instruments at the time were tuned to A=443 and if that was the case, then I suppose it is best to hear it played back at A= 443Hz.