Another interesting question and I've no idea the answer to this.
The records and statistics for professional games in the UK are kept by the Press Association, and I guess it is these records the are used by all the fantasy football games and statistical reports that are published after matches over here, but who actually decides what is and what isn't an assist I don't know.
I guess the PA must have approved record takers, who work to a certain criteria, at each match.
But it has nothing to do with the referee ))