So. What I found:
The tenant had been doing some sprinkler work out front and for some reason wanted to take out the pressure regulator from the plumbing going into the house.
He reported seeing an arc as he was manipulating the components and then got a sizable shock when he grabbed the two components with his two hands (!).
I arrived and saw that the bonding cable for the panel (newish) was clamped to the plumbing on the HOUSE side of the pressure regulator. The inspector for the area wants it to be on the STREET side of the regulator. Me? I like being certain that the plumbing in the house is well bonded. When I do and install like this, I bond on both sides of the pressure regulator and then jump to the ground rod.
I found as many as seven amps running down the ground cable toward the plumbing and the ground rod in the front of the house.
I took the pressure regulator apart and found a 45v potential across the joint, so there was definitely enough there to get your attention, especially with wet hands.
Then I released the grounding cable from the plumbing, and then from the ground rod. And found essentially nothing. Less than three volts. And I could not recreate the 45v I had moments before.
I opened up the panel and got a similar reading. I shut off the main power and got nothing. And both legs were within a volt of the other to neutral/ground. So the power company was absolved.
The tenant's washing machine stopped running and suddenly the amps pouring down the ground dropped to 0.3.
This place was built in the late '30's with flex and cloth/rubber conductors, which are still in place.
I am inclined to expect a system that old to leak about a third of an amp, who disagrees?
I ran the (gas) dryer as well, and it caused the leak on the ground (at the panel) to go up to nearly 4 amps, same as now the washer was doing. I replaced the receptacle, and of course found what modern standards would call a grossly over filled box (cloth/rubber, and the connections are twisted together and soldered, then wrapped in very bulky cloth tape!)
It is an old house with old wiring. A full rewire with a dedicated ground everywhere is in order, but not going to happen anytime soon.