"SHOT" is simply the wording on the Emergency Lube activation button on the overhead panel. It illuminates (I think, if someone has access to the FM and can correct me please do!) when 2 conditions are made: ac is in flight and the MGBP caption is activated, which was the case here.
Vibrations change on helicopters all the time. I don't know if similar systems are installed offshore, but I'm sure if one of them showed a similar change the immediate action would not be "quick, shut it all down, take it all apart and check it" but "interesting, we'll keep an eye on that". The procedures for doing so are well laid out in the aircraft maintenance documents, and in this case it was being done "in accordance with the manufacturer’s maintenance manual."
This is an interesting last line from the report:
"Detailed examination.......of the reason for the indication of a failure in the emergency lubrication system continues."
Not "failure of the emergency lubrication system" but "indication of failure in the emergency lubrication system"? Maybe I read too much into it but are the AAIB currently thinking that the Emblube system was in fact working, but the indications were that it was not, leading the crew to "land immediately".
Obviously no criticism of the crew here, the Emergency checklist is unequivocal in this case and ditching was the only and correct course of action, which they did perfectly.