Anyone believing otherwise is in the wrong gig.
or is an operational SAR crew member because otherwise you would never get airborne.
In the civilian systems I have worked, the management decided what was accepted. I presume here HMG has decided to provide SAR whenever the ground services feel it needed
the call can come in from a variety of sources and there doesn't need to be anyone medically trained on scene so you often launch on minimal information (not even a very accurate position).
If a walker falls and injures their leg and their companion dials 999 - they may think it is a broken leg even if it is just a twisted ankle but you won't know until you get there. At what point do you turn round and go home? A much trickier decision than some seem to believe.
If Emergency services are on scene then the crew can get real-time medical information via Airwave or by phone through the coastguard.
I have been called out to someone who 'had their arm bitten off by a horse' (nothing of the sort, just a fall), 'has been gored by a bull' (got caught between a big cow and a fence) and 'a person trapped in a flooded carpark' (Boscastle). And 250 nm off the West coast of Ireland for a merchant seaman with appendicitis (he walked off the aircraft at the hospital and discharged himself from their care as there was nothing wrong with him). You just never know........