I read both books - "How not to die" (Greger) and "the Longevity Diet" - and I thought about their opinions as well. ATM I tend to stick to good oils from plants as well as nuts. Greger is not very convincing - mostly because he suggests nuts as well, and a good produced oil (like extra virgine olive oil) does not loose much nutritional value. I don't care about reduced antioxidants in oil if I combine it with greens that have loads of them.
Just have a look at the study he mentions when he's talking about the impairment of artery functions after eating olive oil: https://onlinelibrary.wiley.com/doi/pdf/10.1002/clc.49602214...
Quote: "This impairment, however, was also totally eliminated when vitamins C and E were given. As with antioxidant vitamin supplementation, olive oil, eaten with vinegar on a salad, did not impair endothelial function. Some societies that use the Mediterranean diet may have learned to provide the natural antioxidants which buffer the oxidative stress of these fatty meals."
He totally eliminated this aspect so he can ban the oils. Another discussion here on HN blamed him for cherrypicking studies. I'm not sure if that's wrong. He has some good advice in general but for this aspect, I don't really trust him.