What sort of meter is used there?.
My understanding of an energy (KWh) meter, is that it has two coils in it.
One is the Potential coil and that connects across Hot and Neutral.
The other is the Current coil and that connects in series with the Hot wire before it feeds the load.
I'm thinking maybe that the Potential coil may have upset your continuity readings, because of a reference to Ground through the Neutral.
We determined this by simply turning equipmwnt on after not physically seeing any fault in or around the equipment.
Can't say that I like the idea of that technique, because if there had have been a genuine fault on the circuit, things could have happened.