Interesting question indeed... I have just consulted my OM-A with regards to this. While it says that the extension of the duty periods must be "acceptable to the commander after consultation with all other crew members" and therefore lays the responsibility and the decision at the commanders feet, it also says in the section "Crew Health Precautions" as follows: "A crew member shall not perform duties on an aeroplane if he is not able to fulfill applicable medical requirements, is in any doubt of being able to accomplish his assigned duties, if he knows or suspects that he is suffering from fatigue or feels unfit to the extent that the flight may be endangered".
So while the final decision on go or no go is the commanders, it seems that every other crew member coming along for the flight in violation of above mentioned paragraph is violating OM-A rules himself and on his own account.
This leads me to the conclusion that factually, a NO GO can be decided by every legally required crew member while a GO can only be declared by the commander in case of no NO GO has come up. Sure, this might have to be explained without tea or biscuits present lateron, but the OM-A seems clear on this.