Honestly that is the most daft and silly reason Ive seen to open the radiator cap.
the system cannot create a vacuum under the radiator cap if there is a leak (you mentioned water pump) and hence not suck the expanded coolant. its not only PEE DEE AMMS - its a universal thing - if you have a leak in a closed system that is supposed to create vacuum - vacuum wont be created - no vacuum or even a leak in the overflow pipe or a bad radiator cap seal will lead to "AIR" being sucked in instead of the expanded liquid. - hence when you open the cap you see low liquid level because human eyes cannot see air and it is deduced that the system is low.
btw - your car has a heat index? WOW
and you can actually humanly FEEL the extra heat? - dude you are superman. When I work on hot engines - no matter if its 75C or 90C its freaking blazing hot to touch.
After your above comment, I believe you dont know how the system works, if your water pump was leaking you are at fault to keep driving it - with a leak like that you have air which can cause boil over inside the system...