I'd never heard of the direct panzer communication either before seeing this recent documentary series, Clash of Wings. It's presented well, the German aircraft by Ekhard Tolkhan (sp?), and its assertions clear and unambiguous.
It makes good tactical sense, considering the relative lightness of Germany's early war tanks and yet their importance in Wehrmacht strategy. It also displays the nature of the often remarked, unusually close relationship between Luftwaffe and ground forces, when as you mention, other air forces certainly did provide ground support...so what was the difference? According to this circa. 2000 documentary the Stukas were in direct individual contact with panzers, who called pinpoint strikes at will.
"..it was in a sense, a smart-weapon," to quote Ekhard.
As for England, their British narrator asserts a lack of cooperation between ground units and the RAF, giving examples of different doctrines and strategic approaches directly in competition with each other. And of course we know the competition even between individual field commands within the RAF during the BoB, but this was played off well by HC.
I'm not challenging the exemplary and pioneering centralised organisation of the RAF, don't get me wrong. It wasn't until 1942 I think, Germany replicated it in the Luftwaffe.
However the closest direct comparison to such air force/ground forces closeness might be the USSR's doctrine that the air force was an extension of the artillery corps, but this left their interceptor, escort, bomber and fighter squadrons playing catchup to the very well equipped ground attack classes at the start of the Great Patriotic War.
As far as I know even the so named US Army Air Force regarded itself as prone to completely seperate tactical organisation from ground forces.
GB, the US, France and other nations were apparently often at odds between what their air force and army commanders thought was the best way to go about any given objective.
It all sounds very plausable to me...nice simple facts that all by themselves would work precisely as the historical example.
Who knows?