Yes, there have been cases where one has arrived at the piano as a late teenager instead of being a 7-year old, and have succeeded in making a performance career. The problem is that the older the person is, it gets markedly and progressively more difficult to train the hands. I've seen a few people in their mid-30s taking up piano seriously, but as high as the motivation may be and as much as they try to play artistically, there is a certain stiffness or lack of suppleness and dexterity that causes stilted playing that is readily obvious to the listener. So I agree with your premise, but recognizing those parameters too.
Rubinstein's case was different. He started piano young enough and had excellent training from Dr. Barth in Berlin, but he lacked self-discipline in his earlier touring days. He would neglect practicing and be indifferent about the errors he made on stage. Once he got down to brass tacks, he became a renowned artist.
The other very common condition that has existed over the generations is what is sometimes called "low advanced block". That is to say, there are many pianists who reach lower advanced repertoire and play it very well. But they cannot, even with the best teachers, transition into upper advanced (virtuoso) playing. The syndrome has never been well understood. There might be several different causes--a psychological block, inability to cope with the demands of denser scores, lack of desire to invest the necessary time, or whatever else may be involved. But it is a cold reality.
I would say it is self-confidence and mental stamina rather than suppleness. a child can walk on a tightrope because it does not realise it can fall, while an adult will be kept from trying just by the mere thought he might.
What I mean by mental stamina is the power to concentrate long enough on a piece so that no self-doubt creeps up. This is the case with me, at least: my hands never get tired and the arms hardly ever become tense, but it is the mind that falters and then I stumble. If this goes for others, I do not know.