The kind of woods the Mosquito was built, were not readily avaliable for the Germans.
I take it you have definitive information confirming this, because I know that Germany had more indigenous forest available during the 1940s than just about any other West European country, not to mention wood from Finland and all the other occupied countries. As for the types of wood:
http://www.ecotec-energiesparhaus.d...nd-wood-industries-in Germany at-a-glance.pdf
Germany's forests consist of 72 tree species. Of these, 26 non-coniferous and 7 coniferous tree species are used economically. The most important main tree species in this respect are spruce, pine, beech, and oak. Among the coniferous trees, larch and Douglas-fir play an important role in forestry in general, while the silver fir is important in Southern German
The main wood types used in the Mosquito were spruce and birch, and different thicknesses of plywood - European Federation of the Plywood Industry - What is plywood? Possibly the only wood Germany might have had trouble getting was balsa
Even if they had been, the wooden construction is labour-intensive, while the Germans were doing everything possible to reduce the labour needed to produce their aircrafts.
Doesn't really make much odds; Britain had large numbers of experienced wood workers who were quite capable of mass-producing wooden components with the same skill level, and in about the same amount of time as metalworkers could supply metal components. One reason the Germans needed to reduce the labour required was the increased need to use slave workers as the war progressed.
Perhaps because the "myth" has authoritative support
Well let's see the "authoritative support".
...and is based on some fairly simple observation. Pieces of aluminum can be directly printed by a press. Each piece of wood and / or plywood must be sawn and / or bent into the right shape by a worker. Furthermore, at the end of assembly, the aluminum should be just painted, while the plywood must first be covered with glued fabric, another work that must be done by hand (and that, thereafter, makes repairs more difficult).
"simple" observation is right; I guess you haven't seen a woodworking factory or noted that shaping wood with templates can be done as a mass production process no more time consuming or difficult than stamping metal. Somehow the British, Canadians and Australians managed to build over 7,800 Mosquitos, in spite of the poor, hard-done-by workers having to use manual labour.