I can't speak for the signs at Dublin airport, although I may have the "pleasure" of seeing them at the end of August.
However, according to my trusty book, the Aliens (Amendment) (No 3) Order 1997 means that "aliens" do not have the privilege of entering Ireland without passports. "Aliens" are defined by the Aliens (Amendment) (No 2) Order 1999 as those who are not citizens of Saorstat Eireann or British citizens.
As christep rightly observes, "British citizens" is a subset of the wider group of "British nationals" (the ambit of which is not clearly defined anyway), so his British national non-British citizen girlfriend was getting away with it!
However, pace patdavies, "British citizens" do exist (as do "British overseas territories citizens" and "British Overseas citizens") - see the British Nationality Act 1981, as amended by the British Overseas Territories Act 2002.