Since balanced cables predate the GD, this strikes me as an acoustic implementation of an EE concept. Neat!
Being a non-profit facility, there are no fancy DSPs to notch out the hum or anything like that, so more creative solutions were investigated. It was determined through dumb experimentation that orienting an identical microphone 180 degrees to the one with the hum and setting the gain similarly would nearly eliminate the hum.
Eventually, the working theory became that a relatively new large pad transformer installed across the street was being picked up by the microphones. Orienting one microphone 180 degrees from the other caused the hum to be picked up out of phase from the main, and thus could be mixed in to cancel out the main mic hum.
Ultimately the real solution was simply buying better microphones, but there was a period of some months while a microphone sat off stage, pointed backwards.
I would have expected that this decades-old and well established component of power infrastructure would have been commoditized by now and integrated into any dedicated AV performance/production space such as an auditorium.
A simple notch filter won't fix 60 Hz hum. Or, at least, when I've tried to eliminate annoying 60 Hz hum in my own amateur recordings, it's never been very effective. The problem is that the 60 Hz hum isn't a sine wave. It's more like a square, so you've got a bunch of harmonics up the frequency spectrum to worry about too. You can try to also notch out 120, 180, 240, etc. but it starts to get weird sounding fast.
On the same pole facing down at the entire band, you have the omnidirectional mic trying to capture the whole thing as good as possible, suitable for live broadcast from this other channel alone. They didn't have stereo radio yet anyway.
Afterward back in the studio, starting with only the two channels on reel-to-reel tape, the "difference" channel can be phase-inverted to an auxiliary tape, then you have three channels suitable for mixing.
And with analog techniques like this they can be mixed "down" to 5.1 surround sound.
From a single mic stand and only two live signals.
But as for the acoustic implementation, even that has a long history. The Dead borrowed the idea from fighter pilot headsets, the only difference being that pilots were contending with a noisy cockpit rather than feedback. Same general idea that the unwanted sound hits both mics somewhat equally while the voice hits both mics somewhat unequally.
Therein lies the difference between Cat5 and Cat5e: Cat5 pairs were all twisted at the same frequency, while Cat5e pairs must not be twisted at the same frequency.
(This is also how we were able to transition so quickly and cheaply from Cat5 to Cat5e: All that was needed to produce Cat5e on a line that had been producing Cat5 was just a relative speed change on the machines that twisted up the individual pairs.)