Jigsaw was conceived during the last round of cost cutting in the N.Sea. It was intended to replace all of BP's platform and rig staqndby vessels with a helicopter only rescue facility. The thinking was that 3 choppers would be sigificantly cheaper than 20 odd vessels and their crews.
After a fair bit(!) of pushback this was enhanced with 3 supply vessels, each of which carries 2 ARRC (very large RIBS - with a cabin etc).
So it is likely that the ARRC which arrived at ETAP after the ditching had made 'best speed' from where ever it had been launched (they spend most of their time in the davits on the supply vessels).
The supply vessels positions and routing as 'optimised' to maintain the ARRC capability.
Having been involved in some Jigsaw assessment the expectation is you will wait for 2 hours before an 'asset' appears. The original helicopter trials resulted in goos recovery times - how well that is replicated with the same(?) crews involved in regular routings - no idea.....