Some commercial peanut butter may have added oils though there is no reason to add oil to freshly ground peanuts. Many commercial peanut butters have added sugar.
Peanuts have a high fat content. Peanut butter has a high fat content. Low fat peanut butter often contains added sugar to enhance the flavor, usually high fructose corn sugars.
Some markets (*WinCo in my area*) have machines in their bulk produce section to turn whole peanuts into freshly ground peanut butter. This type of peanut butter may separate into an oil layer that can be stirred back into the mixture. The user can control the smoothness of the mixture by removing a portion of the oil before stirring it back in.
I question the claim that peanut butter is made by adding oils to the residue from peanut oil extraction. It would be much cheaper to stop the extraction process while the ground peanuts are still at a useful consistency. It is my understanding that peanuts from which the majority of the oil has been extracted are used as animal feed.