Max pressure is just that, the maximum pressure required to meet the maximum rating of the tire. I would imagine the tires on your son's Tundra have a max rating of around 5,000 to 6,000 pounds PER TIRE at that max. pressure! Seeing how the entire vehicle probably weighs around 6,000 lbs, running at max pressure would be unwise... tread will wear in the center and traction will be compromised.
Long story short, 32 PSI is a good median. If he is towing or hauling a heavy load, upping the tire pressure is a good idea. I would imagine that with a max rating of 65 PSI, those tires he has are 'E' rated? They would be meant for hauling heavier loads, more support under pressure. It might be wise to run higher than 32 PSI if they're E rated.... say, 40/45/50 PSI, feel how they ride and keep an eye on the tread wear. Adjust as needed.