Odds are this is where they are pulling the code from saying you need a vent
507.2.2 Type II hoods.
Type II hoods shall be installed above dishwashers and appliances that produce heat or moisture and do not produce grease or smoke as a result of the cooking process, except where the heat and moisture loads from such appliances are incorporated into the HVAC system design or into the design of a separate removal system. Type II hoods shall be installed above all appliances that produce products of combustion and do not produce grease or smoke as a result of the cooking process. Spaces containing cooking appliances that do not require Type II hoods shall be provided with exhaust at a rate of 0.70 cfm per square foot (0.00033 m3/s). For the purpose of determining the floor area required to be exhausted, each individual appliance that is not required to be installed under a Type II hood shall be considered as occupying not less than 100 square feet (9.3 m2). Such additional square footage shall be provided with exhaust at a rate of 0.70 cfm per square foot [.00356 m3/(s · m2].
The thing is these codes are all for commercial kitchens and you are not a commercial kitchen. Also unless your using open fire to heat your still your not going to get any noticeable heat from it and also no vapor.
Its a tough argument to make with the un in formed fire marshal who also happens to sign off on your project.