Pretty much this. It is actually recommended to NOT install residential smoke detectors in a kitchen area specifically because of nuisance alarms, unless they are specifically approved for use in proximity to cooking devices (page 6 references in the below document references NFPA 72 section 29.8.3.4)
Nuisance alarms lead to systems being disabled... Sound familiar?
For info on nuisance testing see
http://mips.umd.edu/docs/reports/4707_USI_Milke_Report_final.pdf
U of MD by the way is one of a handful of universities that offer actual BS degrees specifically in Fire Protection Engineering.
I would take a look at whatever your local code setting agency (city/county/state) actually provides in writing. The number of people I have met that THINK they know what the code requires is astounding. It is possible they have that requirement, but it seems strange to me.
Maryland has a statewide requirement that adopts NFPA 72. (NFPA 74 which was specific to houses was rolled into NFPA 72 in 1989)
Code compliance is generally fixed at whatever was in place at the time of construction (or major renovation.) So in MD the requirements depend on when the house was constructed. They did retroactively require all dwellings to come up to the 1975 level of at least having a smoke detector though.
Montgomery County hosts the gist of NFPA 72 as adopted by the state (Art 38A sec 12A of the MD State Code) at
http://www6.montgomerycountymd.gov/content/frs-safe/resources/laws/alarms.asp
I will say without a doubt, smoke detectors save lives. Please find a way to get a working system back in your house.