No you are incorrect. It can however depend upon the interpretation of the regulation, but FCL.1000 states:
FCL.1000 Examiner certificates
(a) General. Holders of an examiner certificate shall:
(1) hold an equivalent licence, rating or certificate to the ones for which they are authorised
to conduct skill tests, proficiency checks or assessments of competence and the privilege to
instruct for them;
So to examine for a CPL the Examiner must hold a CPL however; to examine for a rating such as SEP; MEP; or IR, the Examiner must hold an equivalent rating to the one they are authorised to conduct tests for.
The UK CAA has pursued this since the start of EASA regulation and many older Examiners have reverted to PPL privileges.