[bos]

While fun and satisfying, this is extremely unlikely to be true.

The first attested use is from 1945, on the nose of a P-47 Thunderbolt flown by Captain Milton Thompson of the 509th Fighter Squadron. And his art was exactly what you'd expect: a charging bull with the words "balls out".

[inigyou]

Maybe he's thinking of "balls to the wall"?

[bos]

Could be, for which the first attested use is in 1965 or so. Still doesn’t help.