Running at or above the recommended pressure reduces rolling resistance, minimises side wall wear caused by excessive flexing and reduces the chances of suffering pinch flats but I'm not aware of any evidence which shows a reduction in the number of punctures. Above a certain pressure rolling resistance actually increases so 150psi and over is counter-productive and as far as absolute maximum pressure is concerned, the rim will fail before the tyre does.
Anyone remember 'flint catchers'? They were like little off-cut pieces of metal coat-hanger which were adjusted to just skim the tyre tread. The theory being that a shard or thorn requires a good few rotations of the wheel to work its way into the tyre. The flint catcher swept the tyre, preventing the little bastards from penetrating. I wonder why they went out of fashion. Knobbly tyres I expect.