When my family lived in New England, I was quite used to the sight, sound, and smell of fuel oil being delivered via tanker truck every fall. Then we moved to San Francisco, where most home heating was via natural gas. I have never sniffed any benzene in a natural gas heater. My current home has a natural gas heater, and like all other such heaters it is fully vented to the roof. The cooking stove in the main kitchen has a fume hood which works quite well. The water heater, also fully vented to the outdoors, also is natural gas.
The only possible source of benzene into the interiors might be the cooking stove in the main kitchen. However it also has a hood with a powerful blower, that vents to the outdoors, so I'm not worried about that.