I might disagree to it. Though it looks that if the Supervisor Agrees to take you as his student, he cannot guarantee your admission. Getting an admission into the University is your own responsibility. However, generally since the supervisor looks into your academic profile before accepting you, a person makes it through the University Admission Criteria as well.
I remember the Email I got from my supervisor. It said that I have been accepted with funding. But I need to get admission into the University. The only thing in an admission that relates to your supervisor is when you have to mention its name in the application. Thats about it.