Aircraft registered in UK overseas territories (including the Cayman and Falkland Islands) are regulated under OTAR's, which are essentially watered down CAA regulations, administered by ASSI. Google otars and all is there for you to read. The person responsible for regulating aviation in the Falkland Islands is the DCA, Mr. Andrew Newman, based in Stanley.
BIH operate G-registered aircraft, and therefore have to comply with CAA regulations, operating under a British AOC (I think), from which dispensations have to be requested from the UK CAA.
There is certainly one ex RN pilot working for CHC in the Falklands, and I'm sure they have other pilots perfectly capable of adapting to the role, in whatever definition of 'limited' is being used.
The only reason this SAR cover is being set up is because the serviceability record of the MPA machine is nothing short of appalling (I have heard 50%, which surely can't be true?). No SAR cover, no fly, with the result that for every day the oil fixed wing charter is delayed costs £100k - hence the quick fix. However, in the event of a real emergency, I'm quite sure MPA would get the first call, if they were serviceable.
Word on the street is that CHC are broke, and maybe going under?