Yes, in theory it should be extra virgin olive oil. In theory there are people who inspect it. But if they raise doubt about the authenticity of a clearly subpar product, they get sued in a stacked court system. So everyone cheats and nobody calls them on it.

See http://articles.latimes.com/2010/aug/05/business/la-fi-olive... for an example of a lawsuit that was filed over this in the USA. (Because you really can't sue about it in Italy.)

That makes a noticeable difference in the kitchen. Using olive oil you'll find yourself overheating more often. It's also more expensive, and imparts a flavor, which you typically don't want in your oil when sauteing or pan frying. If you want that flavor, pour a little high quality olive oil on at the end. I do that with something like a pan seared halibut, it's heavenly.

Thomas Keller mentions in his books (I believe both Ad Hoc and Bouchon) that he uses canola for sauteing and pan frying for exactly those reasons. (Grapeseed oil is great, he mentions, but very expensive. Peanut oil is typically used for deep frying.) He's probably the most technical of the chefs with numerous Michelin-starred restaurants so I'm inclined to take his advice.