I have read at least one account where anti-aircraft gunners in Europe let an enemy flight pass while firing on friendly aircraft. A publication was produced during the war as described in the following:
"For training purposes, models were especially important — per the
U.S. Army-Navy Journal of Recognition, it was critical that observers be able to see an “object as a whole” and be “able, through
constant practice, to recognize that object (plane, tank, ship, etc…) from any angle.” Initially, the parts-based WEFT recognition system (standing for: wings, engine, fuselage and tail) dominated
training, but it was time-consuming — observers had to recognize then mentally assemble parts to determine the whole. This approach was subsequently discarded in favor of a total-perception
view of recognition, aimed at speeding up the identification process by tapping into innate pattern-recognition capabilities. The
Journal of Recognition also published regular issues to help keep
readers up to date on changes in aircraft design."
Example:
https://www.ebay.com/itm/39384434944...kAAOSwsQ1hx31W