I heard that one a bit differently.
In heaven, the French are the cooks, the Italians are the lovers, the British are the police, the Germans are the engineers and the Swiss run the trains.
In hell, the British are the cooks, the Swiss are the lovers, the Germans are the police, the French are the engineers, and the Italians run the trains...
Your version works, too. The version I mentioned dates reliably to the 1860's. It was contemporaneous with the famous comment of Bismarck when asked in 1864 what he would do if the British landed an army on the Helgoland coast to support the Danes (with whom the Germans were going to war): Why, I'd send the police to arrest them!