It is interesting that the "high fidelity" circuit uses a lousy old LM358 opamp that produces horrible crossover distortion and has trouble with frequencies above only 2kHz.
The circuit is similar to an "echo canceller" IC that is used in telephone conferencing products and high quality speakerphones (Polycom). It builds a model of sounds you do not want (when it is adapting) then cancels them. If something in the room (maybe a door opening) changes the model then the IC goes berserk!
An ECG circuit for showing heartbeat waveforms picks up 60Hz interference from the patient's right leg, inverts it and adds it to the inputs for cancellation.
NONE of my audio circuits have 60Hz interference because they are connected together with shielded audio cables.