The studies I read, there was no ventilation / exhaust fan. The point was that low income households using these stoves often don’t have proper ventilation and it makes them dangerous. I didn’t find much evidence that using them with proper ventilation is actually a serious problem.
Further, cooking releases all sorts of chemicals from incomplete combustion in the air if something is burning, as well as the toxic chemicals release from nonstick cookware at very high temperatures, so cooking without ventilation is bad for your health would be the message I’d take away. I find most people are completely unaware of the hazard.
Very few residences have proper ventilation. In the US, a microwave above the stove is common. Microwave often do have a fan function, but the vast majority don't vent outdoors. I doubt that running air through a very thin filter will do much good.
Yeah I'm not sure what the purpose of the comment was. To convince people to continue using gas on the off chance it won't increase cancer risk? That's not a compelling reason to use gas. It might not kill me.