As a referee, I'd have to say that is totally unacceptable. A referee must make a decision on what he sees. He can make a decision based on what his assistants or the fourth official sees, but NEVER a player.
Imagine this situation: a player comes up to you (the referee) and admits that he struck a player. None of the match officials see the incident. Would you send the player off for that? If you do, suppose the player says that he was just making a joke. Too risky to start using the word of a player. Few goalkeepers would be honest, and even if they were...suppose other teammates disagree; the goalkeeper doesn't always have the best view.