I don’t know how gate staff are still getting this wrong. They should check Timatic and go with what it says. This is what timatic says about a U.K. passport holder travelling to Greece.

“Travelers need a valid passport to enter Greece. The traveler's passport must have been issued less than 10 years before the traveler's arrival date and remain valid for at least 3 months after the traveler's departure from Greece“

Put in a claim for incorrectly denied boarding.