You are misunderstanding what you are reading. P rated tires DO NOT USE THE SAME FORMULA for generating the LEGAL load rating. You are discussing the LEGAL rating and NOT the actual capability to handle a load. LT tires have a reserve of over pressure for their legal "rating" vs P rated tires which do not... but that in no way shape, form, or fashion makes the LT rated tires able to handle the load less than a P rated. Its just a legal difference. To get similar load ratings you must multiply the P rated tire by .9 to get an equivalence.
A tire with a P rating that can handle X pounds is slightly less capable of handling the load as an LT tire rated at 5% less of a load. The P rated tire is less capable at the same pressure as the LT rated tire. See... you do learn something new every day dont you.
To reitterate: LT tires, like commercial motor vehicle tires, are required to have additional pressure, purely as a precaution, and mandated by law. Just becasue P rated tires are not required to have the same extra presure as an extra layer of protection for over loading, does not mean they require less pressure to handle an actual load. A taller, narrower tire will require a higher pressure becasue of its dimensions.
Our trucks have lower pressure in front than rear. This is due to the rated loading for the bed when loaded... it does not make it the right pressure for use with nothing in the bed... again legal vs real.