Perhaps this is where Harmonisation is missing a trick - I am sure that there are opportunities to be more efficient by harmonising all air assets. But at the end of the day, it all comes down to the person who answers the phone. And whoever that may be will always be constrained by their local knowledge, training and operating procedures.
Besides which even a grid reference and an OS map is not always adequate to decide on which is the best asset, not least because the grid reference is often wrong.
In this case it seems a shame that there was a delay between the AA suggesting using a SAR asset and ARCCK actually scrambling Crab. I hope the casualty is making a swift recovery.