To not immediately secure the CVR and notify the proper authorities seems a major misjudgement.
Well, they were requested to contact an FAA supervisor, and even given the phone no., before switching off. When did they call the FAA supervisor? What was discussed?
Not implying anything, but looking at the 'EK / Seychelles' incident, where it was discussed something in the line of "we don't file a report, if you don't either", we simply don't know what the AC crew and FAA super. discussed and what actions followed from that discussion.