After the war, the Allied powers were very skeptical of the Luftwaffe's kill claims, until they saw their meticulous documentation and research. The RLM in Berlin were incredibly exacting in their records, as were their standards. Both the US and the British launched investigations into the Luftwaffe, not so much as out of a desire to prove or disprove the Luftwaffe aces claims, but to figure out how the Luftwaffe, outnumbered and outgunned still proved to be one of the most lethal and most highly organized fighting machines in history.
Both the Allied and the Axis pilots required either a witness and/or gun camera footage to claim a kill. Some of the more prolific aces (Hartman, Galland, Priller) had designated wingmen whose primary job it was to tally their leaders kills.
Moreover, the Luftwaffe initiated a stringent "point" system for their pilots. While the allies branded a pilot an "ace" after 5 kills, the Luftwaffe required many more times this number before the full "Experten" lable would be awarded. Please see LUFTWAFFE SCORE SYSTEM
The book The Luftwaffe Diaries was completed in the 1960's, and documented that the Luftwaffe was not only accurate in its claims of kills by its aces, it undercounted many claims. Moreover, the RLM in Berlin was more stringent in its criteria than either London or Washington.
In short---those Luftwaffe aces were not some figment of the Nazi propaganda machine. They were the real.
I think what they did was share kills. If two ganged up on a bomber, they would both get credit for the kill. So I was told, anyway.
It's hard to know how to compare kills in different theaters, but don't underrate the Germans. One of their aces shot down about 150 Brits, mainly in N. Africa, before being killed. That's a lot more than the top Allied ace (a Russian) shot down.