Every Mode S transmission contains a unique ID that is capable of being used to identify pretty well any civil aircraft by tail number
Certainly every Mode S transmission carries the aircraft id. Using that to identify the tail number is not quite so easy because of the disparate way in which these ids have been allocated and registered.
ATC will not be blamed for incorrect wake turb standards where the FPL has not been amended correctly.
If there is a smoking hole in the ground the blame will be spread far and wide and the smart QC at the subsequent enquiry will only have to ask the ANSP senior manager how often did this happen? with the follow up question what did you do about it? and the blame will very quickly spread that way.
This isn't corrective action it is mitigation.