Common mode noise can intrude rails. Oscillation is not random, its periodic as created by self instability. Looks like a crooked sine or a bad triangle. A scope triggers on it and you won't miss if it ever appears riding on the rails of your equipment.
Short ground needle accessory on naked nose probe helps picking less interference than with probe's neck ground return crock wire. Due to much less inductance and narrow loop area very near to nose pin.Ground pollution it was Yoda says. Disappeared with 200 kHz bandwith limiter. Probe on negative rail
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