I see I'm way late for a timely reply but for future use by others... Yes you have a leak between the submersible pump in the well and its pressure switch on the pressure tank. There is no other possiblity, the only reason for you to question this troublshooting is due to you not undetstanding how your water system works... guys that work on wells do know. And the pump will have to be pulled and hopefully the pump won't drop off the drop pipe if the leak is at a fitting.
Switches rarely fail to open or close and yours was closed which is the only way the pump gets power. The pump was running because the water pressure was insufficient to shut off the power to the pump which is done by raising the pressure to the cut off setting of the switch. You heard water running in the well or the pump running and knew to check for a fixture open in the house. And now you question the well guy... lol yeah I know, you don't want the pump pulled and the cost of it but the electric bill you haven't received yet may show you the error of that thinking.
Quality Water Associates