Ok I'm studying for Air Law PPL exam and reading through the articles see article 32 and Licences of personel.
States - pilot shall hold licences issued by the state in wich the aircraft is registered.
Your quote is incomplete. It says "issued
or rendered valid by the state in which the aircraft is registered.
So for example the US renders your UK licence valid with the paperwork you do at the FSDO before they let you hire the aircraft.