It's more complicated. Olive oil is high in antioxidants. A recent study found that no realistic cooking process would significantly oxidize the pufas in evoo because the antioxidants are pretty good at what they do.
This isn't wrong, assuming that you can get the real stuff. Extra virgin olive oil (EVOO) has a higher smoke point and will survive cooking. Unfortunately, if you purchase olive oil in the US, there's a good chance that it's been processed, even if the label claims it's EVOO! A study by UC Davis found that 2/3 of oils labeled EVOO did NOT meet the standards.
The processing step that the fake oils use will degrade the antioxidant capacity that you'd get from real, cold-pressed oil.
So, in summary:
PUFA's go rancid easily in absence of antioxidants.
Pure EVOO, though PUFA, has antioxidants that protect it.
If you buy "EVOO" in the US, it has possibly undergone processing (despite the label!), which means that it will have lower antioxidative capacity
The processing step that the fake oils use will degrade the antioxidant capacity that you'd get from real, cold-pressed oil.
So, in summary:
PUFA's go rancid easily in absence of antioxidants.
Pure EVOO, though PUFA, has antioxidants that protect it.
If you buy "EVOO" in the US, it has possibly undergone processing (despite the label!), which means that it will have lower antioxidative capacity
Wiki article:
https://en.wikipedia.org/wiki/Olive_oil#Adulteration