No. All the registrar has to do is answer the emergency phone call. Whomever is capable of dealing with an emergency IT situation should also be clueful enough to do something sensible with an urgent request. If he decides it's bogus, he can refuse to act. If he decides it's legitimate, he can take the appropriate action. And if he decides he can't decide, he can defer a decision until he gets some help.
The decision and responsibility still lie with the registrar, but the registrar will have the information passed along by ICANN. In the worst case, the registrar will take two days to process a truly urgent request, which will likely have negative consequences for the registrar, but the pain won't come from the data protection authority. But the likelihood of a worst case is small. There's plenty of room for all parties to communicate and make a sensible decision.
Meanwhile, the contract language will protect the registrar from trolls just trying to make the registrar look bad. And the gathering of data will make future versions of this discussion much less speculative.
Steve