I called an electrician today and they came by within an hour to look at the problem. As it turns out, the electric company did come by at some point but never rang my doorbell or notified me they were there. They added a huge wad of some kind of putty on the line as it enters the electrical meter. I have no idea if the opened the meter and saw mater or if they just mashed the putty on the line hoping to resolve the problem. My electrician took it off to inspect the junction where the cable enters the meter. The new putty was applied on top of the old putty which appeared cracked and broken a bit. They chipped off the old putty and applied a silicon sealant. The meter is locked and can only be opened by the electric company so my guys could not look inside to see if there was rust or water.
However, they did tell me the main cable enters the meter and then splits to attach to the meter itself. So the cable is not sealed all the way from to drop connection to the breaker panel. The electrician assessed the water was entering the cable in the meter box. This seems more likely because the distance the water would have to travel through that cable to the basement, while traversing a split in the cable itself inside the meter would be unlikely. If so the sealant they applied should resolve the problem. It will rain here tomorrow so I will have a chance to find out.
I also learned that the electric company owns the drop to the house, as others mentioned, and the meter. But the wires from the drop connections to the meter and the wiring from the meter to the breaker panel are my responsibility - which is weird since the meter is locked and the cable I am responsible for enters that box which I do not have access to.
In any case I hope it's fixed so I can close the panel up and not worry about my water alarm waking me in the middle of the night again.