Italian leather is a marketing phrase before it's a material specification. Hide imported from elsewhere and tanned in Italy is still legally Italian; hide raised in Italy but tanned elsewhere is, in most brand-page usage, not. The phrase is most rigorous when the brand pairs it with a town: Solofra for clean smooth calf, the Santa Croce sull'Arno cluster for vegetable-tanning, certain Tuscan houses for the soft-pebbled finishes you see on a Mansur Gavriel bucket.
What the careful brands disclose: hide origin, tannery region or city, tanning method, finish. What the marketing brands disclose: "Italian leather." The gap between those two disclosures is most of what Cousure's material transparency rating measures.