I was wondering if it is possible to play a four hands piano piece with just two hands. Were any classical musicians capable of doing that?
Short answer: yes, but...
Longer answer: A piece for piano four hands generally has movement of notes in opposing directions that can "tie up" a single player's fingers, and/or spans of notes that two hands generally cannot cover. Depending on the piece, it is possible for a single player to improvise something similar, but they probably won't hit every note on the page and so the harmonies and movements won't be as "deep" as with two players.
There is a famous story about the blind jazz piano player Art Tatum. When he was a child, circa 1920, he heard a piano piece from a player piano roll. It was recorded by two pianists playing four hands on the piano. However, Tatum did not know that it was a four-hand piece, and had no sheet music (which he could not see anyway) so he learned it by ear and played it by himself, with two hands. This is recounted in the Jazz documentary television series by director Ken Burns.
However, in a quote from a published book mentioned in the Wikipedia article on Art Tatum, it's said that Tatum himself denied that this story was true.