I don't know that I'd go so far as to say it's the prerogative of the chair.
I can say that no chair has ever done that. It has happened that there has been consensus that was not unanimous, and that too is not all that frequent because there is usually the agreement of everyone around, but not always. My experience has been that the chair will expect agreement among some opposition members and some government members—let me put it that way. It's not a one-sided thing, because consensus with nobody is consensus with yourself.