They can peer with large local providers / exchanges and rent some of their local storage capacity without owning that equipment, and without having corporate presence in Italy. (You don't have to be German to rent a Hetzner server, do you?)

That's enough of a corporate presence. Whatever they have in Italy can be shut down. You don't get to not follow the law just because you're buying from a vendor.

Enough to shut down by ordering that the local providers stop providing service to Cloudflare; likely not enough to sue Cloudflare proper.

Not a big difference for the customers in Italy.