It is seems to me to be clearly not true
What is your reasoning/proof behind this thought? As far as I can see it is true! Is there a physical explanation why not? Quite often reality flies in the face of ‘common sense’!
why dont we all just ride skinny road wheels if we get the same grip footprint whatever size tyre we use?
This bit doesn’t make sense to me!
On road we want minimal rolling resistance, therefore require high pressure. Narrow tyres can more readily/safely be inflated to higher pressures for various reasons, and so are better suited to road riding. You get a small contact patch due to the high pressure. On a smooth surface grip is not strongly related to the contact patch size.
Off road, because the ground is bumpy, a lower pressure, wider tyre rolls better. A lower pressure also gives a larger contact patch, and hence more grip (because both the tyre and ground are not smooth).
So, in summary, you get nominally the same contact patch for any two tyre diameters/widths at the same pressure. The thing is, nobody runs large tyres at high pressures because it defeats the point of having large tyres. Nobody runs narrow tyres at low pressures because it defeats the point of having narrow tyres.