No, Kaine just thinks Peter is the clone and Ben is the real deal.
Before the Spider-Man clone later known as Ben Reilly, there was the enigmatic Kaine. Kaine was the Jackal's first temporary success at cloning Peter Parker, but the cloning process was flawed.
Over time, Kaine degenerated, leaving scars across most of his face. The Jackal tried to kill the clone, but instead, Kaine grew stronger, eventually surpassing the strength of Spider-Man. When the Jackal used the perfect clone against Spider-Man, the ensuing battle left the clone and the Jackal for dead. Behind the scenes, Norman Osborn managed to have the files switched, so the Jackal would think Peter was the clone and Ben was the real deal. Consulting the Jackal's files, Kaine also believed the same, so he followed Ben Reilly through his "exile", and has framed Ben for murder, hoping to give who he thought was the clone, Peter, the life Kaine could never have. Kaine was responsible for the apparent death of Elizabeth Tyne, the love of Ben Reilly's life, and tried to kill him countless times.