The excellent T.V. series 'Apocalypse - World War I' states that he was buried in the New Zealand section of the graveyard with full military honors and a ritual mourning ceremony from Maori troops - as shown in this short silent film clip - but I don't know.
The burial video is Australian War Memorial sourced and I cannot distinguish detail between the BEF ANZAC troops shown - but it is claimed that he was most likely shot-down by Australian anti-aircraft fire .. I'd take that as an indication.
However, there is also a report that von Richthofen managed a controlled crash- landing in that field and was shot by a Canadian soldier as he tried to get out of the plane.
Australian Slouch Hat.
I understand that all three Nationalities wore the slouch hats (as did Gurkhas)... and further more - the men on active service would have been issued with a variety of replacement equipment
Puggaree.The 'puggaree' (hat band) would be a distinguishing feature but I regret that the style also has varied considerably over the time period. The following detailed clarification doesn't help me very much.
"There seems to be some confusion in the some of the comments about who was wearing what style felt hat in the NZEF both prior & during WW1. To clear this up for those who aren't quite sure, most NZEF units that embarked for overseas duty in 1914 were issued with & wore the typical Slouch hat with raised rim to the LH side, hitched with a short leather strap to either a lions head hooked badge or a regimental badge with a hook attached ( now very rare ). The Wellington Infantry reg & some Artillery units were known to have worn the Lemon Squeezer at this early stage of the war. By 1915, several other units were adopting the LS as shown in photo's of NZ troops at Gallipoli. By 1916, general orders required that all sectors of the NZEF ( with the exception of the Mounted Rifles ) would adopt the LS as standard head dress, the MR would continue wearing the Felt hat with a bash fore & aft without a raised rim. Although the are some period photo's showing the LS being worn by MR as well ( unofficially ).