I read:
I'm just curious as to how some piece of external hardware would know what is feedback and what is, say, just an electric guitar holding a sustained note...
well you wouldn't put the feedback eliminator in the guitar mixing path in the first place I guess ;)
other than that those boxes don't _know_ what the feedback is, that's what the knobs on them are for to adjust the tradeoff you are inevitably having when removing parts of the frequency band.
regards,
x