Well, sort of :) Kevin Rudd (our former Prime Minister) is somewhat famous for saying "fair shake of the sauce bottle" in a TV interview, instead of the saying "fair suck of the sauce bottle".
The "correct" version refers to sharing booze between friends, but Kevin Rudd's version meant sharing a bottle of tomato sauce (or Ketchup as you would say) to put on a meat pie.
People made fun of him for being too damned "clean" - ie. was he so PG rated that he couldn't even allude to consuming alcohol?
I thought your "fair shake" may have been in reference to that.