Just to get it out of the way first, a K&N drop-in replacement (I'm not talking about one of the those cone filters) doesn't not flow better then a brand new traditional paper filter. What the K&N does do better is over the course of a filter run, the paper ones become clogged and dirtier then the K&Ns, and that's when the K&Ns flow better.
About MPG, sort of correct. Simply put it takes __quantity of air + __quantity of fuel, to make __horsepower. Correct that everything is corrected by the computer. The computer, to a point though, can adjust the air/fuel ratio. The claimed savings comes from the timing. Because of the higher a/f ratio, the computer can advance or retard the timing (at what point in the cylinder stroke the spark plug ignites). That is where the supposed savings comes from.
In the real world you are likely to not notice anything. The only gains you would notice, are if the old filter was a restriction. Under anything but heavy throttle, it usually isn't.