Flavio
Perhaps not quite as surprising at it may seem, since Air Britain's books are either about the aircraft and the units and not about the claims made by these units.
For example claims by 806 Sq is mentioned rather superficially and cannot (and should not) be taken as any final "official" claims summary.
With regard to the aircraft book 'FAA aircraft 1939 to 1945' I believe no mentioning is made in relation to pilots claims vs aircraft. Mind you I have not gone through every page checking that!
Only those pilots known to have paid the ultimate prize in relation to a known s/n is mentioned.
I don't think Air Britain has ever published a single book about aces, claims etc since that is not the primary goal of the Society.
While not having the 806Sq book myself, I am quite confident that both Cull and Galea have done their "homework" pretty well. They are quite well known for that!
Cheers
Stig