annary, I'm going to confuse you more, sorry!
Advice is contradictory in the UK and Germany. Over there they don't do it, over here they do. I don't put oil in DS' food, but I do put butter, but only for flavour purposes. If you ask a doc, a midwife or other German mothers, they're going to tell you to put oil in the food.
Just do what you think it's right for your DS.
HTH