Don't forget... when the US boys appeared in the skies above Europe there wasn't much to shoot at anymore.
Largely true. Chuck Yeager famously shot down five 109s in a single battle when he stumbled alone into a German squadron (a feat which is pretty common among the best aces of any country, including the Germans). But due to a lack of Germans he just didn't have nearly enough opportunities to repeat those kinds of stunts.
I think the last big impression by the Luftwaffe was at the battle of Kursk, after that it was barely able to defend anything.
Eh... after Kursk the Luftwaffe was certainly crumbling, but it wasn't
crumbled. It was really
Big Week which delivered the real death blow to the Luftwaffe. Everything after that was one prolonged death rattle until
Boddenplate which was the last gasp.
So because the Soviets overestimated their kills, Germans didn't overestimate theirs? That's not even close to logical.
When it comes to air-air combat, the key to kill overclaiming are really the pilots. Overclaiming is reduced the better your pilots are, with the kill claims of aces being far more accurate than the average. A new and inexperienced pilot was likely to overclaim by 500% or more, a veteran likely by 200-300%, but the best aces only overclaimed by only about 20-30%.
Marseille, the German ace who scored most of his kills in North Africa, and for whose victims we have the best records for, claimed some 158 kills. Post war research has verified over 100 of those kills, leaving about 50 in doubt, of which in only about a dozen cases is there absolutely no way Marseille could have shot down as much as he claimed. A portion of the remaining claims may still be kills, but while they cannot be completely discounted, it's impossible to conclusively attribute them to Marseille. In particular, on the single day when Marseille claimed a stunning 17 aircraft shot down (and the rest of JG.26 another 9) Allied records show 23 fighters were indeed shot down in that area, making it possible that Marseille did in fact shoot down all, or nearly all of his incredible one-day total.
Other Allied aces whose claims have been scrutinized against German records show a 60-80% verification rate, so Marseille's over-claiming by as much as a third was nothing out of the ordinary. For an ace. Because of this most people take the claims of the top aces as generally accurate, and there's no serious movement to officially adjust them.
The hows and the whys of this are actually pretty simple. The best aces invariably had superb eyesight and were fantastic shots. They tended to hit what they shot at, and usually hit it lethally. And they also had the vision and the situational awareness to make a pretty good assessment on how much damage they'd actually done. Poor pilots on the other hand tended to spray hails of bullets at the enemy, and record any indication of a hit as a kill. In many cases what happened was the inexperienced shooter had not landed enough rounds in a vital location to bring down his target, and the damaged enemy dove away to escape, being subsequently mistakenly recorded as a kill.
The point is that the usual rules of overclaiming don't apply to aces. If you want a rule of thumb then reduce their claims by 20-30%, but even that still leaves the German experten with colossal totals. Some salt is still required, but not much of it. By and large what research we can do has shown the aces did indeed shoot down most of what they claimed.