Troubleshooting Noise/Quirks in Audio Circuit
Number 3 answer: the ESD diodes on input and on output are the path. Your line-level is a volt or two. Diodes turn on (exponentially, true) at 0.5 or 0.6 or 0.7volt, and once on, the opamp's internal rails (+15, -15v) have a distorted version of the input.
With the +-15 volts wiggling, the output bipolar devices try to turn on at peaks of the audio.