We've had that question before and the answer is no. No concert pianists started from scratch from say the age of 16.
I dont know if I agree 100% with things stated as absolutes. Anything is possible, they said nobody could defeat the best trained army in the world (Britan), least of all a small group of farmers, and yet here I live in this place called America.
I would say again, anything is possible, but the next question that must be asked is: "Is it very probable?".
That answer is a function of: practice time available, focus, DESIRE/Resillience, natural talent/ability to pick things up quickly, marketability and the quality of your instrument.
Available Practice Time: Some one who has a family is less likely to achieve their goals as quickly as someone who tons of free time on their hands. How much time is needed? That depends on your natural talent and focus.
Focus: I would bet that I can achieve more in a single year of focused study than years of mindless studying.
Resillience: Theres an old saying "As a man thinketh, so is he." If you have an almost obsessive compulsive disorder (OCD) with music then it doesnt matter what people say, your going to do it.
Natural Talent: Mozart had a huge amount of natural talent and picked up his skill very quickly. I believe genius will shine through no matter what age you start. Einstein couldn't read until he was 6; they closed the patent office in the 1800s because "everything that could be invented was already invented".
Marketability:Im sure there are many adults who didnt start as children who are virtuoso pianists the problem at that point as others have stated is competition or as I would say marketability. I was watching the 9th van cliburn competition the other day and for the life of me I could not tell the difference between last few pianists, it was as though they played identically. But they all couldnt win. I personally believe that the pianists who have a very unique and different story to tell from their identically talented peers are the ones who go on to become famous because they are the most memorable.
I hope this helps. I started late 15, and I plan to become a concert level pianist virtuoso. I just dont care if I'm as famous as horowitz or if I go on tours, although it would be nice.