A classic scholar has proved the point, by unearthing a Greek version of the world-famous piece that is some 1,600 years old.
A comedy duo called Hierocles and Philagrius told the original version, only rather than a parrot they used a slave.
It concerns a man who complains to his friend that he was sold a slave who dies in his service.
His companion replies: "When he was with me, he never did any such thing!"
The joke was discovered in a collection of 265 jokes called Philogelos: The Laugh Addict, which dates from the fourth century AD.
Hierocles had gone to meet his maker, and Philagrius had certainly ceased to be, long before John Cleese and Michael Palin reinvented the yarn in 1969.
Their version featured Cleese as an exasperated customer trying to get his money back from Palin's stubborn pet salesman.
Cleese's character becomes increasingly frustrated as he fails to convince the shopkeeper that the 'Norwegian Blue' is dead.
The manuscripts from the Greek joke book have now been published in an online book, featuring former Bullseye presenter and comic Jim Bowen presenting them to a modern audience.
Mr Bowen said: "One or two of them are jokes I've seen in people's acts nowadays, slightly updated.
"They put in a motor car instead of a chariot - some of them are Tommy Cooper-esque."
Jokes about wives, it seems, have always been fair game.
One joke goes: "A man tells a well-known wit: 'I had your wife, without paying a penny'. The husband replies: "It's my duty as a husband to couple with such a monstrosity. What made you do it?"
The book was translated by William Berg, an American classics professor.
(Thanks Shawne F)