A story for the masses is necessary and this doesn't appear to be a bad stab at one. Harry can always bring trusted others on board by telling them what actually happened. He might have actually done that already and this is their plan. How much time did Harry have to do stuff before needing to show up anyhow (40m? 50m?)? Also, Prof. McGonagall is terrible at faking anything so telling her the truth before this seems like a bad idea.