I think the substance of the science discussed revolves around the composition of dietary fat. As the article notes, the recommendation for increasing the proportion of "polyunsaturated" oils is likely a major factor. Indeed, common vegetable oils contain a high proportion of linoleic acid, the "base" omega-6 dietary source. It has been shown in numerous studies that the omega-6 (N-6) to omega-3 (N-3) ratio is important since these essential fats are linked to immune system functioning.
N-6 fatty acids are associated with pro-inflammatory factors, N-3 primarily leads to anti-inflammatory products. In the archaic/traditional diet, N-6 and N-3 were present in roughly equal proportion, but with marked increase in vegetable oil consumption, N-6 to N-3 becomes "imbalanced", e.g., 10:1.
Inflammatory processes are well-known to play a role in cardiovascular disease, so it's not hard to see how increased N-6 fatty acid intake is a contributor. However this info has not been a secret in the fields of obesity and metabolic disease treatment and research, where the impact of dietary fat intake has been discussed and published for more than 20 years.
Since the mid-90's I've recommended sharply reducing polyunsaturated vegetable oil intake as part of "lifestyle" changes supporting optimum health, particularly for patients with predisposition to metabolic disease. FWIW I've followed my own advice for at least as long, the results have impressed my internist who jokes that I've become quite an uninteresting case.
(Don't have references at hand. If anyone wants I'll post them.)
Artemis P. Simopoulos, An Increase in the Omega-6/Omega-3 Fatty Acid Ratio Increases the Risk for Obesity
Tani S1, Takahashi A, Nagao K, Hirayama A, Association of Fish Consumption-Derived Ratio of Serum n-3 to n-6 Polyunsaturated Fatty Acids and Cardiovascular Risk With the Prevalence of Coronary Artery Disease.
Khan SA, Ali A, Khan SA, Zahran SA, Damanhouri G, Azhar E, Qadri I, Unraveling the complex relationship triad between lipids, obesity, and inflammation.
For all the good things people say about the fat composition of olive oil, canola oil is probably better. It also has a more neutral taste. It's all refined though, and a GMO, things which some people don't like.
Anti-inflammatory diets is about the only way to survive into old age regularly, in both the length of life, and the quality of life aspects.
The main reason is that these are supposed to produce less cancerogenic compounds after high temperature treatment* and they also do not leave any strong specific taste.
Both do not contain significant amount of omega-3 fatty acids, but the cooking oil probably also should not be your main source of fatty acids anyway (usually we wipe the products clean after cooking).
Perhaps somebody else could give better insight into it.
* I actually have not researched this deeply, but these oils do have relatively high smoke point https://en.wikipedia.org/wiki/Smoke_point
If your goal is to minimize aldehydes produced in cooking coconut oil is maybe best but can affect the taste. Lard and goose far are good alternatives that for some foods can provide a better taste.
Edit: Lard and Butter also work quite well.
Edit: Geese might disagree but they're mean.
My understanding is that peanut oil is very pro inflammatory and a bad idea to use at high heat. Butter, animal fats and coconut oil are my go to oils. But I don't deep fry.
I would add to that "most", had a stomach ulcer, no bacteria detected in multiple tests.
Turned out my stomach produces excess acid when I'm under stress.