For a wee bit of background, this machine was operated on behalf of Strathclyde Police and was basically dedicated to the West and part of Central Scotland. At Uni we done the financial case for the first machine they leased, as it was a (depreciation calculation) cock up, but I remember clearly the territorial scope.
The other Scots forces were pretty small (Strathclyde was second only to the met) and never had air support.
In April 2013 the forces merged into 'Police Scotland' and I assume overnight that the machine started being dispatched all over the place - including Dalkeith.
I don't really know, but all of a sudden having a bigger territory and potentially (just a guess) no plans for fuel pick ups East / South / North of the notional base is perhaps a factor relatively new to its operation, albeit the air ambulance operated by Bond from the same base always had a wide territory
That's not to say that other forces may have requested air support in the past, but I would have thought that this would only have been for more serious issues.
Hopefully this answers some of the 'fuel base' queries, though as I understand it wasn't the lack of fuel on board that was the issue, just its location.