Exist: to have real being

It would be as you say if "real" were defined as simply " having existence", but that is not so, and the definition insists that the existence must be objective, independent. Taking the example of this legendary personage named King Arthur, that exists only as a legend it can't be said to have an objective independent existence because it depends entirely on the imagination of medieval man.

Here "objective" has to be taken as meaning this.

(SOED) 2 b […] external to or independent of the mind.

As King Arthur is a personnage that never existed outside of a reality solely in the mind of man, it can be said that he is not someone that ever had real being.