I've commuted on 23/ 25 tires inflated to 100-115 PSI for the last 6 years and can probably count the flats I got during my commute on one hand.
I also used those Specialized Armadillo tires on a century ride and hated them. I got them specifically for their puncture resistance and got three flats that day! I eventually called the SAG wagon because I had ran out of patches and tubes!