There were other stories – Jazz Muller trimming his hedge with his lawnmower; Kevin Skinner taming the Bok in '56; everything Colin Meads ever did – but Conway's coolheaded sacrifice topped the lot.
The version I heard was that Conway broke his finger working on a farm (of course!), the pinky getting mangled in a farm machine. In its most well-buffed form, the legend had it that the farm machine came off second best (makes sense!).
So off went Red to the GP. "Sorry mate," says the doc. "There's no way this will heal in time for the South Africa tour."
"There must be something you could do, doc?" implores Red.
"Nope," says the doc, and then laughingly: "I mean other than cutting the thing off!"
Conway looks him deadset in the eye and slaps his mitt on the doctor's desk.
"Get cuttin'."
The truth is more prosaic. The finger had been damaged not in agricultural service, but through years of playing softball, in which sport Conway was a catcher.
On his Rugby Remembered Facebook page, sports journalist Ron Palenski tells it straight: "In the summers, [Conway] was a softball catcher and one of the occupational hazards of the position is getting the ball in the hand that doesn't have a glove.
"The third finger of his right hand was sprained and then broken by balls which whacked into it. The break mended but the finger had a permanent kink and a surgeon told Conway that if he continued to play football, it would break again.
"With the prospect of the tour of South Africa in 1960, Conway decided to get the digit lopped off. The deed was done between the final trial and the naming of the team."
It was the great Manawatū philosopher Mark Shaw who said of being an All Black: "You've got to be prepared to piss blood to wear this jersey."
Pissing blood is one thing. Unsure of how many would sacrifice a body part? Red Conway put a finger on it.