The reason some people think overinflated tyre have more grip is the same reason people think low profile tyres have more grip. They are more responsive.
In real world conditions where the roads aren't perfectly flat and have loose gravel a properly inflated tyre will give more ultimate grip because they will conform to the road.
Easy to test if you can find a deserted roundabout and see how fast you can go until the tyres start to let go.
My old van use to have 2 inflation pressures on the placard for heavy 60psi and light loads 45psi. It was very tricky to drive in the wet with 60psi but completely different car at 45psi.
Competition tyres are sometimes designed to run higher pressures so they stay attached to the bead under high cornering loads. They make up for the loss of grip with soft compounds. I had Tarmac rally tyres on an old Datsun for a while, you don't know what grip is until you've tried them
