I don't even know if it would be possible to prove it true even if it was.

But very often fighter engagements ended with neither pilot being able to hit the other, until one or both ran out of ammo or fuel. Or, one pilot realized he was outclassed or in a disadvantageous kinetic energy position so he just ran away or hid in a cloud.

In the case of fighter escorts of bomber formations, the job of the escort was to protect the bombers, not shoot down his opponent. If the bomber completed his mission, the escort fighter completed his, even if he wound up shot down himself.

For the defensive fighters, the ones going after the bombers, their mission was to shoot down bombers, if they wound up in a fight with an enemy escort, they failed, even if they won the dogfight, because the bomber would get through.

It must have been tough for fighter pilots defending their homeland. Not only did they have expose themselves to escort fire, to ignore the attacks of the escorts and make predictable formation attack maneuvers, and not defend themselves, they also had to contend with the bomber's own gunners.

In a full dogfight, top engine performance mode and high maneuver environment, planes went through a lot of fuel in a hurry, and they usually carried less ammo than for 60 seconds of continuous fire.