Could I conceivably use power from my neighbors (hypothetical) solar panels in the event of a blackout?
There is disconnecting hardware to prevent backfeeding into the grid when the power company loses power. These disconnects are similar to the transfer switches required on generators. The disconnecting device is usually or can be locked and inspected by the utility that feeds the grid. It would be highly illegal and dangerous to try and bypass any of this equipment. Just run some extension cords from you neighbor to your house.