Oil pressure is higher than water pressure. If the crankcase is pure I would vote for a very tiny leak in the oil cooler. It has probably been leaking a long time and only the most exotic pressure test will make the leak show up. My experience has been that a head gasket problem will be more likely to pollute the crankcase with oil.
My son just bought a '92 for $900. 00 because the water had oil in it. When he called Cummins the shop boss told him that he had never seen anything but the oil cooler cause oil in the water IF the crankcase was pure. The new oil cooler seems to have been the cure. BTW my son's friends all hate him now.
To get the oil out of the radiator and heater and engine and hoses use automatic dishwasher detergent and plan on flushing the system every time you drive it far enough to get it good and warm. It will take a number of flushings to clean it all out. This, of course, is after you replace the oil cooler. The reason you want automatic dishwasher detergent is because it will not make suds and cause you grief.
I don't know where you are located, but make sure you don't freeze your truck and break expensive things while you are cleaning the cooling system.