I'm not the only on who didn't understand this one.
I admit I have no idea what's going on. Even if I was at the job I couldn't just go straight to the problem with the information given but I could trouble-shoot and find the probelm.
It's an old house with old wiring ( see it all the time ). Did you take the conductors loose at the panel and check continuity to see if say the hot and ground were shorted or the neutral and ground ( not all shorts are dead shorts that would trip a breaker )?
You say this is a circuit feeding the counter top. Experience tells me that back in the good old days when this house was wired there is no telling what all is on that circuit. When trouble-shooting forget all about code and what should be there and try to figure out what's really been done. Old houses are a trip and you can find all sorts of weird wiring. You trace the circuit and just see where it leads you.
A few years ago I had a problem it an upstairs bathroom and the circuit ran in PVC out through the back yard and had been damaged when they were grinding strumps. Not what I expected but that's where the problem lead me.
When you know you have a problem you follow it and find the cause.