"I am still confused about one thing though...if the water had to be turned off to the radiator, how could they have heated the space?...at least during the time when the pipes actually froze?"

Quite true...although the OP have also claimed that they have "not now or ever heated the apartment". They then mention "it never occurred to any of us to turn the heat on for the night" which would imply there was some type of heat source available to them.

Gail