It was not a Puma. Puma’s go to theatre by C17.
Larger types such as CH47 and Merlin require a much larger degree of engineering work to fit them in the back. It can be quicker to self ferry instead of taking them to bits, rebuilding them and doing the air testing.
A couple of years ago the Puma fleet trialled completing more major engineering work in theatre. This meant more people away from home and in the threat than necessary. Being further from the supply chain incurred unnecessary delays and on the whole it did not work.
None of the above indicates a shortage of helicopters but we all know that the fleet does need to be bigger to cope with increasing demand.