Leaving aside the questions about the production of Berluti's RTW shoes, it is common practice to produce goods (at least in parts) in some cheaper labour countries. European Union rules allow merchandise to be labelled "Made in Italy (or wherever)" if "significant production" has been made in the country in question.
It is perfectly legal to produce a shirt somewhere in the third world, and as long as you cut the buttonholes and attach the buttons in Italy, you can call it "Made in Italy". Lots of manufacturers exploit this loop hole. Unlike the fibre content and composition of the fabric, you are not obliged to show the place in production on the label. Quite a few firms leave that out. Hackett, who once proudly proclaimed everything to be "Made in the British Isles", is one of those. Country of origin gets only shown if it is prestigious, otherwise it is just left out. As I said, "Made in xxx" does not necessarily mean, the item has been made in its entirety in the country in question.
The story goes that Bernard Arnaud (LVMH) did the Victor-Kiam-Remington-thing ("I liked the shaver so much, I bought the company") on Berluti shoes (the firm was on the brink of insolvency and Arnaud was worried his favourite shoemaker might go under). LVMH, and Mme Olga as the public face, have done a remarkable job. Of course they have used plenty of BS to muddy the waters ("the colour get bleached by the moonlight").
I believe (and of course Berluti will not give you any factual information) that "Venezia" leather is basically a crust (undied) leather, not dissimilar to the leather EG uses. It is the firm's choice to split it to that particular thinness.