Shaman,
If the pilot is an employee of Ryanair he will receive a P60 from them with the tax deducted in Ireland. He then needs to send that P60 to the Italian authorities where they will tell him how much he owes and also the the Irish authorities where they will send all the tax bakc to him.
If he is a contractor under the BRK technically he has a contract for services with a UK company and therefore he has UK sourced income and woudl need to file a return in the UK and then in Itlay.
Under the BRK recomended way then the employment is as per the first way above. Instead of Ryanair the employer will be the company one of BRK's accountants have set up.
It therefore leads on that Her Majesty's Inland Revenue are wasting their time "going after" the brookfield pilots. If they do then BRK up sticks and either move to Ireland or half way to the Isle of Man. Then the IR have nothing to do with them.
If you pay for advice as my guy did you will be told that every piece of EU taxation, employment and company legislation says that what BRK is doing is wrong. However the cold simple fact is that BRK are in a position to bully any one individual pilot and the Unions are not going to help.