Yes, you could be right. I know at one time years ago there was information on it. I looked around while we were discussing it and could find very little. Most sources are not sure and say it could be either one or maybe something else. I think reading the history of Casey Jones and his steam engine operating the term all-out, balls-out,balls-to-the-wall or some such thing was used a lot as he drove em hard and fast.
The legend himself Jay Leno explains what the term "balls to the ball" or "balls out" means.
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term's etymology:
On old steam engines, there was a governor device that had an arm with two steel balls on each end. This spun around, and as the engine went faster the centrifugal force spun the balls higher and higher. When the engine reached its maximum safe power, the balls would be spinning fast and high. When they reached a specific height, a spring would shut down steam and not allow the engine to blow up (over speed itself). So "balls to the wall" means: as fast as the engine possibly can go.
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History of steam engines
When engineers asked mechanics at what speed an engine was running, they’d reply, “balls out” or “balls to the wall” to indicate it was humming along at full steam.
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I followed about a hundred links and no accurate confirmed sources were found for the expression 'balls to the walls'.
These all all mentioned. They are order of first mentioned date.
1. fly-ball governors, balls full out was the top speed setting
2. uk foot ball, balls out
3. WW2 US submarine engine room crew, balls to the wall
4. Viet war bird pilots, balls to the wall
5. The sound of the ball Earth theory being smashed, BALLS to the Wall