In a general sense Balsa 'is' wood and plywood is layers of wood glued together and cross grained with each layer. So truthfully it was made with 'plywood' and to the layman this was enough explanation. I think that was how it was described in the newsreel stories which kept stories simple.
I have read that the 'plywood' used in the Mosquito's was balsa skinned with more traditional plywood.
Don't forget all the life rings and rescue rafts that were made of balsa in the time of WWII.
Balsa trees do grow rather quickly (one of the reasons for its low density) and thus it is not quite the same as an oak or other hardwood to replace.
The growth of balsa trees is quite interesting as it is different than most trees. check out
Quote from Wikipedia on the construction of the Mosquito:
Construction
"The bulk of the Mosquito was made of custom plywoods. The fuselage was built by forming up a plywood made of 3/8" sheets of Ecuadorean balsawood sandwiched between sheets of Canadian birch. These were formed inside large concrete moulds, each holding one half of the fuselage, split vertically. While the casein-based glue in the plywood dried, carpenters cut a sawtooth joint into their edges while other workers installed the controls and cabling. When the glue was completely dried, the two halves were glued and screwed together. A covering of doped Madapolam (a fine plain woven cotton) fabric completed the unit."
Robert