I suspect that the media have grossly exaggerated a minor niggle among some coastguard staff. The 'form-filling' probably simply involves a few quick clicks on a computer screen, to ensure that someone takes responsibility for ensuring that the relevant safety procedures have been complied with.
Anyway, stupidity among the rescue services is hardly new. 40 years ago, I was listening to the old 2182Mhz emergency frequency, and monitoring a rescue mission where aircraft where trying to direct lifeboats to a ship in distress. For over an hour, the (American) pilot of one of the search aircraft reported that he was circling above the lights of the stricken ship, while the coastguard directed three lifeboats the location he'd given. Eventually, a lifeboat coxswain radioed the coastguard to ask if the coastguard had actually bothered to check those coordinates against a chart, since his boat seemed to be heading straight towards the flashing light of a lightship!
Chris