From what I have read, increasing the tyre pressures reduce the grip and the braking ability. By increasing the inflation pressure you reduce the tyre's footprint which is your only contact with the road. Anyone who has had a puncture and tried to brake will know how the deflated tyre grips and pulls you to that side. Okay, higher pressures increases the steering response but again that is because it has reduced the grip. It is the reduced grip that gives you the increased fuel figure.
Here in the UK there is a lot written about over-inflated tyres increasing wear in the centre of the tread.
This next image shows the footprint with reference to the pressure.
I checked my tyres today and the maximum safe pressure, as marked on the sidewall is 44 psi. I run mine a couple of pound over the manufacturers recommendation but that is all (34 instead of 32).