Training can go a long way in developing a good actor. However, great actors are those who stand out. There are several great actors who have no training at all. And even those who do have training have to have something more to be one of the greats. When you think of the true greats, they are the ones that are truly one of a kind.
I don't think you can naturally teach someone to be a great actor. The same thing that applies to athletes. You can't just teach someone to be a great athlete. Sure, you can teach them to get better, but certain characteristics have to be present long before that. Great actors have a natural gift.
Not all great actors are beautiful, and not all had any formal training. It is some combination of talent, no fear of being in front of the camera, confidence, the ability to learn lines, and the ability to connect to audiences. Formal training doesn't hurt but much of good acting can't be taught.
The variety of factors that make actors great proves that there is not a solitary "it" factor that a person must possess in order to become great. Some great actors achieved this status simply by being chosen for a part in a great movie. Beauty and intelligence is not shared by all great actors, nor is political or social status.