You are correct - In the 2009 code it doesn't say a thing about your ventless heaters. That was changed in later codes, though; see the 2015 text below.
602.2 Residential occupancies. Dwellings shall be provided with heating facilities capable of maintaining a room temperature of 68°F (20°C) in all habitable rooms, bathrooms and toilet rooms based on the winter outdoor design temperature for the locality indicated in Appendix D of the International Plumbing Code. Cooking appliances shall not be used, nor shall portable unvented fuel-burning space heaters be used, as a means to provide required heating.
Exception: In areas where the average monthly temperature is above 30°F (-1°C), a minimum temperature of 65°F (18°C) shall be maintained.
^^^ That bolded text in the last sentence is not there in the '09 code.
Perhaps your town has updated their codes. Perhaps your inspector recently took a class on the IPMC that taught him the later version. Or perhaps he thinks you're a poor landlord, and that you should put some dang heat in the apartment that you're trying to make money off of?