Lesser pressure doesnt always mean bigger contact patch. During emergencies, what do you usually do? You hit the brakes hard. So all the momentum goes to the tyres and in particular the sidewalls. So what happens in a soft, squishy underinflated tyres? It caves in in the middle of the contact patch. (Its a bit hard to describe without a picture or diagram) Thats why you usually see skid marks having two dark lines per wheel or side - just before it ends at the armco.
Higher pressure provides for more tyre stability from deformation so comparatively, you get a better, firmer, more even contact patch (therefore better grip) when you hit the brakes or at the limits. Only offset is that you have a slightly more bumpy ride on KL roads. (Oh yeah, you reduce the risk of a blowout or wheel damage if you have more pressure when you hit a bad pothole - something we all face in a 3rd world country...)
Hope that explains. If not, im sure someone else who can explain well will jump in.