Well, I'd say they're wrong and the science of engine operation would back me up. I would also say that the mod has small effect on mileage, and even when you don't change anything on the car you can easily see a 10-15% variance in your MPGs from tank to tank. Tons of things effect mileage, and with a small modification its very hard to see how the mod has effected things.
Below is what is called a brake specific fuel consumption map for a Ford 2.0L zetec engine, but most others are very similar. On the vertical you have your output torque, along the horizontal you have rpm. So, its basically throttle input vs rpm (full throttle = peak torque). What the map shows is grams per killowatt hour you get from fuel. So its the amount of fuel spent per the amount of power you get out of it (aka lower is better, less fuel for more power). As you can see higher engine loads (more throttle) gives you better efficiency (as per the straw example in the last post). Its simply how engines work.
I guess I don't understand, people on a bunch of forums who have put on a CAI say that at certain speeds they could use less gas to go the same speed if they use a stock induction system. and if they used the same amount of throttle, then there speed and rpms went up slighty. hmm
those people think (mistakenly) that the amount of the pedal is a direct correlation to how much fuel is being used. And that is absolutely incorrect. The pedal only decides where the throttle plate is positioned. So with a intake that breathes better, the same amount or more air is going into the engine with less pedal position, however the amount of gas the injector sprays is in direct relationship to the amount and type of air that is getting in.. not entirely on the throttle position.
so an dramatic mathematically incorrect example is if the stock intake at 50% throttle allowed the same amount of are as a cai does with 40% throttle. the engine is now going to use more gas at 40% (the same amount of gas it used to us at 50%) throttle to compensate for the extra air, based on o2 and maf (or other sensor) readings.