It is there, but it seems to conflict with what the CAA seem to be saying.
Part MED.A.025:
MED.A.025 Obligations of AeMC, AME, GMP and OHMP
(a) When conducting medical examinations and assessments, AeMC, AME, GMP and OHMP shall:
(1) ensure that communication with the person can be established without language barriers;
(2) make the person aware of the consequences of providing incomplete, inaccurate or false statements on their medical history.
(b) After completion of the aero-medical examinations and assessment, the AeMC, AME, GMP and OHMP shall:
(1) advise the person whether fit, unfit or referred to the licensing authority, AeMC or AME as applicable;
(2) inform the person of any limitation that may restrict flight training or the privileges of the licence, or cabin crew attestation as applicable;
(3) if the person has been assessed as unfit, inform them of their right of appeal; and
(4) in the case of pilots, submit without delay a signed, or electronically authenticated, full report to include the assessment result and a copy of the medical certificate to the licensing authority.
(c) AeMCs, AMEs, GMPs and OHMPs shall maintain records with details of medical examinations and assessments performed in accordance with this Part and their results in accordance with national legislation.
(d) When required for oversight activities, AeMCs, AMEs and GMPs shall submit to the medical assessor of the competent authority upon request all aero-medical records and reports, and any other relevant information.
On page 6 of the EASA Opinion (Opinion 07/2010 13 Dec 2010), para 28 bullet 3, it says: [my underline]
It is commonly recognised that the complete medical history of a pilot is highly important for the assessment of fitness to fly. Pilots have a free choice to visit any AeMC or AME in Europe and the medical certificate will be accepted in all Member States. The AME may not have the full medical history of an applicant or, for language reasons, may not be able to understand evidence a pilot may offer for clarification. In such a case, the AME can turn to the licensing authority of the pilot for advice on the medical history. Also, the licensing authority is in a position to evaluate the outcome of a medical assessment if it holds the results of all aero-medical assessments the pilot underwent.
This seems to be perfectly clear that a pilot may go to any AME in Europe and that, whilst "highly important", a complete medical history is not a requirement or the AME can revert to the Licensing Authority.
brgds
421C