Not an issue for me at this time- but it appears to have been so for him.
What I suspect was done:
The machine is wiped down thoroughly with a solvent for several minutes, then the solvent is wiped off and the machine allowed to air dry.
Why the above did not work:
The solvent soaks into the metal pores and filler and dissolves part of the oil. The solvent on the surface is wiped off. The solvent in the pores and filler evaporates off this wiped surface- leaving the oil it dissolved at the surface. If repeated many many times, the oil would eventually be removed.
What should have been done:
Mix the solvent in with whiting (calcium carbonate, powdered chalk) to make a paste, and "paint" on the paste. The solvent soaks into the pores and filler. dissolves the oil, and as it evaporates off leaves the oil at the surface of the paste- not the surface of the machine. Remove the dried paste and repeat. The whiting is very white- but will be yellow where the oil is left on the surface. This allows you to know what areas may need more treatment. Whiting is not something most people have on hand, but many other things are. Any powder that is fine enough to make a paste and stay in place will work if it does not interact with the solvent. I have used flour, corn starch, corn meal, baking soda, baking powder, sawdust, bentonite clay as a powder and crushed up "oil dry" to make a powder. I have also laid down "kleenex", paper towels, and strips of toilet paper wetted with solvent.
Whiting can be used in the laundry, but I cannot tell you how because X----X Google assumes I must be looking for bleach ads, want white clothes or am fishing for whiting... I did find out that it is also used with window glazing, making stained glass windows- and powdered chalk is used by gymnasts- and to mark fields, if you want a 50 lb bag.
This method is also a good way to remove oil soaked into concrete. Products such as Oil Dry work the same way- but MUCH slower due to the size of the particles, and not having the solvent. They will work much better if crushed or ground into a powder with your foot, then soaked with a solvent.
I first read about this method using whiting and a solvent to remove oil from military gunstocks prior to refinishing. It works.