Backfeed voltages on dead legs?

I had some tenants move out and 2 months after the fact I'm tired of running extension cords to the unit (which I've been told is illegal, BTW). Anyway, the electric company came out today to hook me up and refused to because of a 26.7VAC and a 22.3VAC backfeed voltage across both legs. It's an Edison split transformer and the main legs were completely disconnected. How could there possibly be a potential difference? Do I have magic wires or something? THESE MAINS WERE COMPLETELY OUT OF THE BOX. I can't emphasize that enough. They share a common run with another unit's conduit and the ground hasn't been inspected. What could be causing this spurient voltage? Give me some ideas before I give up and call an electrician. Bad meter socket? Failed ground (center tap should take care of that)? Induction? There really is nothing more I can think of, the damn mains were in my hand, dead, and still measuring voltage at the socket but not at the end of my mains. Has to be in the socket, right?