The reason people often swear off using oils on their skin is because they're choosing the wrong ones. The chemical composition of the oil they use is especially important- every skin type requires a different ratio of linoleic:oleic acid, and it's your job to find out which one works best for you.
As many who are familiar with this topic know, oleic acid is your omega-9 fatty acid, whereas linoleic acid is your omega-6 fatty acid. According to research, "Acne patients have... been shown to have low levels of linoleic acid in their skin surface lipids." Source. I've read that if you have fairly oily/sticky skin, your skin is higher in oleic acid, which means that you should be topically applying linoleic acid. Here's a list of oils higher in linoleic acid:
Safflower oil (organic)- Oleic (8-30%); Linoleic (68-85%)
Black Seed oil- Oleic (22.6%); Linoleic (55.6%)
Hemp Seed oil- Oleic (10.71%); Linoleic (56.48%)
Evening Primrose oil- Oleic (8.4%); Linoleic (72.6%)
Pomegranate oil- Oleic (6.2%); Linoleic (7.1%)
Sesame oil- Oleic (39.21%); Linoleic (45.69%)
Pumpkin Seed oil- Oleic (23.3%); Linoleic (57.2%)
Rosehip Seed oil- Oleic (13.9%); Linoleic (44.1%)
Grape Seed oil (organic)- Oleic (16.2%); Linoleic (70.6%)
Soybean oil- Oleic (22.72%); Linoleic (70.6%)
Castor oil- Oleic (3.93%); Linoleic (4.32%)
Another study I've found is a wealth of information in reference to oils on your skin. You can find it here. But if you're too lazy to read the whole thing, I'll summarize it for you. Note: EFA= essential fatty acid.
It states that "patients with acne have been shown to exhibit inadequate levels of EFAs such as gamma-linoleic acid in their skin surface lipids, thus contributing to the severity of the condition... Topical supplementation with botanical sources of omega-3 and omega-6 EFAs can dramatically improve the skin of your acne patients without causing breakouts."
Here is a list of oils high in omega-3's:
Hemp seed oil
Red and brown algae
Rose hip seed oil
Walnut seed oil
Wheat germ oil
-note: these oils are "an example of the beneficial use of traditional acne ingredients combined with moisturizers containing botanically derived EFAs and oils."
Oils high in omega-6's:
Apricot seed oil
Evening Primrose oil
Pumpkin seed oil
Rose hip seed oil
Wheat germ oil
-same note as above ^^
In the text itself, it says that Borage Seed oil is a great source of linoleic acid, which also contains omega-3; grapeseed oil is another oil high in linoleic acid, and is apparently important to supplement in the skin of those with acne.
Coming back to the oily skin, sebum which is produced as a result of high levels of oleic acid is often dense and sticky; however, sebum produced with high levels of linoleic acid is less "dense" and more liquid, which is far more soothing to the skin because the follicles have much less of a chance of getting clogged, and as a result less chance of being inflamed/irritated.
Another oil the text talks about is Marigold flower oil, which "displays anti-inflammatory properties while also fighting bacteria when applied topically... Studies have shown that marigold oil stimulates cell regeneration and epithelialization, making it important in the clearing of acne lesions as well."
You can come to your own conclusions about this, but as long as I've provided you with information to get your brain going, I'm happy! I welcome any thoughts/comments as well. I am only educated about this by reading articles and such on the internet, so if I am wrong about anything I've cited, please do tell me.