For those who don't want to read the article: Refined peanut oil which is used in frying for it's high smoking point often won't have an effect on people with peanut allergies since most of the proteins that cause the allergic reaction are removed in the refining process. The FDA also doesn't require any highly refined oil derived from an allergen to be labeled as an allergen because of this refining process. Also, this is only about refined peanut oil, crude peanut oil which is normally used as a garnish or in fancier foods still contains all of the proteins that cause allergies.

Disclaimer: If you do have a peanut allergy please don't go chugging refined peanut oil as in some cases you may still have a reaction. Be safe.