Nich-av,
Nobody can prove you wrong when you're never willing to admit that you are on even the smallest of points, which is pretty apparent.
Pilots working for a UK company that subs them out to NJE on a contract basis are not subject to Portuguese income tax. Neither are the United Airlines ticket agents at Heathrow subject to US income tax. It's really pretty simple.
It kind of goes without saying that the UK tax relief is only available to those who live in the UK. I suspect the reason you can't get your head around it is that you assume the Cadet FOs can live anywhere.