LEVEL is fine. Certainly no reason to take a connecting flight in order to avoid it.

Instead of making assumptions, which might be incorrect, just look through the website to be sure what is included and what isn't.

Your first incorrect assumption has led you to post in the Iberia forum. Yes, the companies are related and the FT mods won't usually move LEVEL-related questions elsewhere... but you won't earn any miles, receive elite benefits, etc. "operated by Iberia" means little more than the fact that the employees work for Iberia and the planes are owned by Iberia.