True, but in normal operations (i.e. not an emergency situation for the aircraft), the controller is very likely to have the better overall understanding.
At the risk of fanning the flames here, I can't let this go unchallenged. Risk management is more than just a binary state of emergency or not-emergency. It's never as clear cut as that.
A controller is likely to have a more complete picture as regards collision risk. But collision risk is a rather small part of the overall risk management picture in aviation -- what proportion of fatal accidents are the result of collisions? The other risks to an aircraft can often only be appreciated by those sitting in the cockpit.
Those controllers and pilots both have incomplete understanding of the entire picture -- different views of the same picture. Most of the time, that doesn't matter, as the actions required are consistent with both risk management views. In cases where the views conflict, mutual understanding is required. Too many controllers out there obsessed with separation for separation's sake, too many pilots obsessed with the needs of their own aircraft.