This all basically breaks down to a lack of coordination in sharing information between agencies and inter-agency. This is a fact of life across the board everywhere. Sharing and coordinating information within an agency (especially at the Federal level) is haphazard and non-coordinated a majority of the time. Trying to share information between multiple agencies invariably leads to these types of situations.
If you can wave the magic wand froggie and solve this age old info sharing dilemma; it is my opinion this will solve these types of situations far faster and in a more appropriate manner than any other actions taken. You cannot realistically pin blame on any one group if timely, relevant, and consistent information is not shared and provided with all parties involved. I understand people need appropriate training. However, I have seen time and time again where no amount of training helped in a situation when inaccurate or no information was provided. Actions taken by all parties involved would have been more relevant and accurate for the given situations if timely consistent info would have been shared with all parties.
Regardless of any specific training provided to any one group, unless relevant and timely information is shared with all involved in these types of incidents, it will all provide a setup for major complications! You cannot function in the blind no matter what training you may possess. Law enforcement, ATC, and the PIC could only act on the information provided (or not) to each. Each was provided with fractional pieces of information. The quality of actions is only as good as the quality of information provided.