Smallwheels,
Imagine the complexity of the electrical wiring in a big two story apartment building, and how easy it would be for the builder to mistakenly connect a neighbor's heating (or A/C) system to your meter's circuit. If your heater is in a mechanical closet directly above your downstairs neighbor's heater, it would be very easy to connect the upstairs heater to the downstairs circuit and vice versa.
I have personally diagnosed that situation in a rented apartment. We were getting huge electric bills no matter how much we tried to conserve. Turned out, the upstairs neighbor's A/C was running off our power, and vice versa. We demanded that the landlord send an electrician to check, and the electrician said this situation is quite common.
What you can do is watch the outside meter when your heater is running and when it's not. If you see it spinning fast when your heater is supposed to be off, investigate further.
I'm not saying this is definitely the problem, but maybe it's worth checking.