Never suggested it was, but the CAA represents a State that is a signatory, EASA does not represent any signatory!
EASA represents 27 signatories to the Chicago Convention (the EU Member States) which have adopted legislation appointing it to carry out certain functions on their behalf. Regional cooperation on aviation safety regulation is encouraged by ICAO and their are similar arrangements elswhere in the world, eg the Eastern Caribbean Civil Aviation Authority.
It fails to recognise ICAO licences issued by member States and insists that the holders have to change to an EASA licence!
The Convention only requires States to permit aircraft registered in other contracting States to make flights across their across their territory and to make non traffic stops. The Convention does not grant the right to base an aircraft registered in one contracting State in the territory of another contracting State. It also gives contrating States the right to refuse to recognise foreign licences issued to its citizens.
The EU legislation on pilot licensing does not require EASA licences for the pilots of aircraft exercising rights granted under the Convention. What the legislation does is to require EU residents who operate aircraft in the EU to have a licence issued/validated in accordance with EU requirements. This is consistent with the requirements of the Convention as such pilots are not exercising rights granted by the Convention.