Tires age-out as well as wearing out. The rubber loses its ability to deform, and cracks instead. I believe this is due not only to time, but also to oxygen and UV radiation. The problem is very greatly exaggerated with soft-compound racing tires, but still can occur with regular street tires. Especially when they sit outside.
Higher tire pressures would, in theory, have very little to do with this phenomenon. It could even be argued to help, because the higher pressures would keep the sidewall from deforming as much, tearing the polymers in the rubber.
IMHO, if you see visible cracks on the sidewall, the tire is done.
But then, I tend to use and abuse my tires more than the average driver...
-soD