EastCoaster - interesting question. Here in the UK controllers are not permitted to initiate reference to "centrefix" because there is no laid down defined point of a particular "centrefix". Also it can be a different point for particular aircraft operators or even different types used by the same operator. Added to which there are no promulgated procedures here using a "centerfix."
If a pilot requests permission to route to the "centrefix" we are supposed to confirm the location so that we can take it into account when controlling the flight in terms of terrain clearance etc.
In my limited experience of pilots requesting to route to a "centrefix" it is a point on final approach anywhere between an 8-10 mile ILS final and I wouldn't clear a pilot to the "centrefix" without the expectation that he will be able to carry out the approach without delay.
Therefore I am not totally surprised to hear that has been confusion about whether or not a pilot has been cleared for the approach.