Crab,
This may sound snotty...but is not meant to be.
If it was within range of the UK assets as you say.
The USAF was on a 24 hour notice status.
How could they be "quicker" than the UK assets?
We have to assume the UK assets being dedicated SAR units are on a quicker response status than "24 hours".
There must be more to the situation than is described thus far.....could you clarify what else affected the sequence of events that led to the longer notice unit being the one used to carry out the task.