This term significantly predates airplanes all together. The term "balls to the wall" originated with James Watt's invention of the centrifugal governor used on early steam engines (circa 1774, well before the Wright brothers at Kitty Hawk). Over the years, these types of governors were adapted for use on various other types of engines, including many aircraft engines. Some aircraft have a ball shape at the end of the throttle control, which is actually a clever reference to the governor mechanism, no doubt conceived by a witty designer. It is easy to see where one could get the (wrong) impression that "balls to the wall" would indicate the position of the throttle lever, when in fact, the term, strictly speaking, is a reference to the position of the weights on the governor.
Increase engine speed! Balls to the wall!