I got to thinking about this. It makes perfect sense that the
oil pressure is higher than the water pressure so the
oil pumps into the water. However when you shut an engine down the
oil pressure goes to zero nearly instantaniously, while the water pressure in the radiator may take an hour to come down. Water being thinner than oil would easily squirt through the same crack that the oil came through. So with this being said, there should be water in the oil, too.
I think if it were me, I would look real hard for evidence of water in the oil. If I found zero water there, I would clean and flush the radiator real good. With the radiator/engine drainded, I would do a pressure leak down test. If it held pressure, I would refill it and see if the oil came back. You never know about dirty tricks. It is possible that someone poured the oil there, and there is nothing wrong with the car.