You're assuming the tailpipe emissions are based on buring the same amount of fuel and not driving the same amount of miles.
Emissions tests are done on fixed dynomometers. They are not done on a "mileage" basis. You cannot confuse work done with emissions created. They are not the same thing and they are NOT related.
The fact is that to achieve the same amount of work you must burn 1.38 times the amount of CNG as gas. This means that the engine, all things equal -- displacement, rpm, etc. -- will have to operate for a longer period of time to achieve that work. It is the TIME that the engine runs which determines the amount of emissions created. An engine that is not running creates zero emissions and will do so for the entire time the engine is not running.
Now, there IS this to consider if you will:
An engine running on alcohol must have the carburetor jets modified to a larger size due to the difference in BTU output. The same should be true of CNG. This means that the use of the 1.38 gallons of CNG would, indeed, burn in the same time frame as a gallon of gas. HOWEVER ...
ONE gallon of CNG, by known standards, would not create the same amount of work nor carry the vehicle the same distance as ONE gallon of gas. The vehicle running on CNG would find itself stalling out and stopping far behind the vehicle running on gas.
Let's take two vehicles which run on the two types of fuel. They both have exactly one gallon of fuel. They both start at the same point and travel at the same speed until the one gallon of fuel is depleted.
Let's say that the vehicle running on gas gets 100 mpg. When the one gallon of gas in this vehicle runs out the car will stop 100 miles from where it started.
The same vehicle running on LNG, which has only 72% of the BTU output of the gallon of gas, will only travel 72 miles before coming to a stop.
At this point, you have to put in another .38 gallons of CNG to get to the same point as the vehicle which runs on gas. The time to get to that point will be 1.38 times the amount of time it took the gas vehicle to get to where it now rests. During this time, the CNG vehicle will be creating emissions.
If the emissions are only 80% of the amount created by the gas vehicle, but the car takes 1.38 times as much time to travel as far, then the emissions will exceed the amount produced by the gas vehicle by 10.4% (.80*1.38 = 110.4).
You simply cannot discount the amount of time that an engine is running regardless of the amount of work produced. The engine produces emissions only when running and it runs for a period of time.