Would this be a good way to visualize it?
Think of a car as an audio system and the road represents your power/electricity. The car/audio system has a level of maximum performance it can achieve. But you can only get the best performance if you drive on a very good road. If you drive on a road that is in bad condition, you can't drive the car to its fullest potential. So even though the electricity going through the power cables in not part of the signal path, it can still effect it.
Think of a car as an audio system and the road represents your power/electricity. The car/audio system has a level of maximum performance it can achieve. But you can only get the best performance if you drive on a very good road. If you drive on a road that is in bad condition, you can't drive the car to its fullest potential. So even though the electricity going through the power cables in not part of the signal path, it can still effect it.