Good that you mention it, I should have done that. Yes, virgin olive oil itself has a high breakdown temperature and is fine for cooking. It's just not recommended for deep frying.
As a comparison: unrefined sunflower or rapeseed oil for example are not suitable for heated foods (although both can be expected to be refined, if not stated otherwise). When they are refined, they are fine for even deep frying.
One interesting thing I found: According to the wikipedia smoke point chart, unrefined rapeseed oil is fine for cooking. My german source says it's not.

My sources: English: https://en.wikipedia.org/wiki/Template:Smoke_point_of_cooking_oils
German: https://www.alnatura.de/de-de/magazin/warenkunde/warenkunde-erhitzbare-oele/