I have a pretty strong doubt that the emissions from gas + cooking are significantly worse than the fine particulate put off from cooking methods like pan frying or burning anything even slightly.
There is also probably a statistics abuse here with the "emissions while not in use" is more likely large rare leakage incidents rather than median kinds of events. Keeping in mind that the amount of methane lost to the atmosphere from petroleum production is absolutely enormous, undercounted, and would certainly dwarf any gas leaks from your kitchen.
But this is the kind of "bad for you" thing which appeals to many people that want to do good and are easily sold ideas by others who don't know what they're really talking about but are good at getting attention.
There's plenty of evidence out there that fine particulate has a significant impact on long term health.
You can easily measure the impacts of cooking by buying a particle counter and making some stirfry or burning some cookies in the oven. I have, it's easy to measure PM2.5 air quality in your apartment worse than the worse city in the world after a bit of pan frying which if you don't actively do quite a bit will linger for hours.
You'd have to come up with a model of nitrogen oxides produced by gas stoves and their long term health effects and compare them to fine particles in poorly ventilated / filtered air in homes.
There is also probably a statistics abuse here with the "emissions while not in use" is more likely large rare leakage incidents rather than median kinds of events. Keeping in mind that the amount of methane lost to the atmosphere from petroleum production is absolutely enormous, undercounted, and would certainly dwarf any gas leaks from your kitchen.
But this is the kind of "bad for you" thing which appeals to many people that want to do good and are easily sold ideas by others who don't know what they're really talking about but are good at getting attention.