I always thought that when people talked about “owning one’s swing”, they meant something like this:
To know the what, the how and the why of your swing inside out, and being able to perform accordingly. When it comes to your swing, there can be no unanswered questions. Nothing can stand in the way of you and the most efficient motion possible given your physical and mental capabilities.
I found this interesting quote in an old article about George Knudson:
“What is it that allows a golfer to own his golf swing? When you consider there might have been only three or four in the history of the game, the answer isn’t as complicated as you might think.
It means repetition of the highest level.
It means a swing plane that is not rerouted and does not change regardless of the club.
It means impeccable posture and perfect balance.
But most importantly, in the cases of Hogan, Moe and George, it means a perfectly square clubface approaching impact that remains square through the shallow, long and low action after impact. One need just look at pictures of the three of them in action.”
~ Irv Lightstone, 2006 (source)
So Irv looked at what (he thought) were the similarities between the golfers who supposedly owned their swings.
So in the end it comes down to this:
Perfect execution of perfect technique with perfect consistency.
In my opinion, achieving this can only be helped by really knowing the what, the how and the why of your swing.
Or else just beat a lot of balls.