I have a very difficult time believing that synthetics would have that much effect. However, when I changed over, I got several mpg increase. It was on a fairly new car, though, so I attribute it to more fully being run-in (some people refer to this condition as break-in...run-in is the same thing to me). PLUS, I started using Fuel Power. PLUS, it got warmer...so, even though I was now running the AC, less dense warm air combined with a possible change-over in fuel composition, combined with all the above, and I saw mpg go from 33 to 37.6 mpg on the same long trip with the cruise control set. Then, there are the variables of the way you car is sitting when filled up, as well as the temperature at fill up and the flow rate of the pump, not to mention the depth at which the nozzle protrudes into the filler hole. Oh, and wind direction/speed.
Take my original 37.6 mpg trip. I got 37.6 mpg on the return trip. Sounds fairly accurate, doesn't it? Still, it wasn't scientifically done, so I cannot argue that it is factual. Very nice coincidence, for sure.
Again, just because mpg changes when you change one variable, it doesn't mean it wasn't some other variable(s) causing (or at least contributing) to the change.