There are many tales of broken guitar amps that allegedly led to the “invention” of distortion. Let’s look at three of them more closely.

Ike Turner
There’s “The Tale Of The Amplifier That Fell From The Top Of A Car”. The song involved in this tale is Rocket 88, recorded 1951 by Ike Turner. One version of the tale says, that the amplifier fell from the top of a car. Another version says, that the amplifier was in the trunk of a car and that it was damaged by rain. In both cases the damage to the amplifier allegedly led to the distorted sound.

Bob B. Soxx & The Blue Jeans
Then there’s the “Tale Of The Speaker That Broke During Recording And Caused Distortion”. This tale is related to “Zip-A-Dee-Doo Dah” (1962) by Bobb B. Sox and the Blue Jeans. The distorted guitar was played by Billy Strange. And Billy Strange himself tells on his forum how he really created the distorted sound:
“The story has been told so many times that now it was a broken speaker cone. WRONG!!! (…) It was a 6-L-6 tube that I pulled out of my old Fender Twin amp to get that fuzz sound on ‘Zip-a-dee-doo-da’!!!.”