While I don't know too much about the piece in depth, I do know that it is usually considered to be on the list of pieces of standard repertoire that you can sometimes "fake," so if Kissin's recording doesn't follow your score, it's entirely possible that he decided to not play what's written! That being said, it would most likely be much more beneficial to you to obtain a copy of the full score of Petrouchka and compare the reduction to the orchestration. That way, you should be able to pick out any blatantly wrong notes right away (like missing accidentals) while getting more acquainted with the piece, and if you should like to add a little bit (like Kissin did to the left hand), then so be it.
Remember that the 3 Movements is nothing but an arrangement of the orchestral score, and the performer is always free to arrange an arrangement.