As a music major on an instrument other than piano, the threat of failing my piano jury and not getting my degree loomed over me throughout my stay at Penn State. So I took piano lessons from one of the grad assistants -- one of the less distinguished ones, unfortunately, but that made us even, as I was certainly one of her less distinguished students. I do remember that she bad-mouthed Van Cliburn via "piannissimo praise", the preferred defamatory gambit of music students. Nobody could speak ill of Cliburn's talent, but the word on the studio floor was that he was "selling out" -- booking too many concerts, which kept him from putting in the preparation necessary to churn out great performances.
Well, sorry, but who can blame him? As Jerry Reed sang, when you're hot, you're hot, and Cliburn was hotter than Elvis. But my piano teacher, amidst the cattiness, let loose an interesting comment: allegedly, Cliburn would often be so "unprepared" as to memorize piano scores he had never actually played on the airplane en route to his gig. The nerve.
The remark had exactly the opposite effect on me that was intended. I could not grasp the level of genius it would take to be able to memorize a piano score that one had never played, or the level of showmanship it would take to perform it. My respect for Cliburn went up, not down.
And yes, even several rows back, one could see what enormous hands Cliburn had -- he was said to have been able hit an octave and a fifth with one hand. You don't have to have huge hands to be a great pianist (e.g., Alicia de Larrocha), but it has to help. The Air Force band to which I belonged once accompanied Leon Bates (back when he and I were both young) performing Gershwin's "Rhapsody in Blue"; Mr. Bates is a smiling, handsome fellow who looked like he would have been as much in his element running a football through a tough defensive line as tickling the ivories in black tie. His style made marvelous use of his mesomorphic build: large, muscular, commanding. Yes, big hands have to be helpful at some level.