Oil in my radiator

When a engine is running the higher pressure oil would go into the lower pressure water. When a hot engine stops the residual pressured water goes into the zero pressured oil. Soooo, the very first thing I would do is drain the pan and look for water in the oil.
Now me... I recycle to reuse coolant whenever I can. My very best method/effort doesn't always get 100% of the oil out of that coolant. What oil that does remain ends up in the coolant recovery bottle. After pulling it and washing it out a couple times, its all clean again. Of course the small amounts added are always virgin stuff.
If you didn't reuse coolant, didn't use a oily funnel, don't have any other explanation, I don't have one either. good luck though.