Dear 'hermanoto',
sorry for long delay. It took me a some time to check, if my source -a magazine article about the 'Carrozzeria Barbi'- is right or not. I've found another picture of the puzzle car of far better quality in an Touring-book, showing definitely the Touring-emblem on the engine hood. Furthermore, there is no Barbi-bodied 6C 2500 listed in the 'AR 6C 2500'-book.
So, I think, a mistake happened by the contributor of the magazine-article, designating the puzzle car wearing 'Barbi-bodywork'.
Of course, the point is yours!
P.S. There are some visible differences to the Touring-model in your photo on the rear of the puzzle car. Behind the door. The puzzle car wears definitely a longer wheelbase. Maybe 'Barbi' did these modifications.
Notes with a proof, as to whether 'Carrozzeria Barbi' was involved in this Alfa-bodywork are accepted with joy