You are correct about your CNG (Natural Gas) running Honda Civic in terms of it polluting less; when operating efficiently. Typical a CNG vehicle can reduce smog-forming emissions of Carbon Monoxide (CO) by 70 percent and Oxides of Nitrogen (NOx) by 87 percent. This is however assuming the CNG engine is burning the natural gas efficiently.
The smog test is just as important on CNG vehicle as on gasoline vehicle. The smog inspection has been put in place to monitor for degradation of a vehicles emission control systems, which can happen to a CNG vehicle or any gasoline driven vehicle.
In this specific case in order to find out which specific emissions component caused the visual inspection failure on your natural gas powered Honda Civic failed you'll need to converse with the smog technician who inspected your vehicle or have a smog check repair station conduct a diagnosis. Also, your VIR (Vehicle Inspection Report) which you should have received after your Honda's smog check should indicate which functional test your vehicle failed. It will not tell you what is specifically wrong with the emission system; it will simply mention the emission system involved.