I just had to get in here on this one even though I have not participated for awhile.
Peter, I agree with you . I have been using Baby Oil for years. The only difference is that also immediately wash out ALL of the oil til squeaky clean with Dawn Dish Liquid. I should do a commercial for all of the times that I have used Dawn and told all of my students to do so. They come back with wonderful comments. Some say that they tried my plan on old brushes and made them usable again.
So, thumbs up on Baby Oil and Dawn. I have saved brushes for years due to that I believe.
Marvin, I do agree too that one needs to clean out the oily content no matter what anyone uses. Also, in my studio, I often use Turpenoid to clean and still finish with Dawn.