I am sorry but based on my experience I think that this is not really accurate.
Just like any other shop, when taking orders they will obviously be more prone to reserve coveted items to loyal and returning customers, and these are obviously more likely to be locals. Just the same happens to shops in the US, in Asia, in Russia, or anywhere else in the world.
But if you happen to step in when they have items in stock you will be able purchase them just like in any other Hermès boutique. As simple as that.
Apart from that, they will obviously have a tendency to answering NO if somebody steps in and asks for a Birkin, probably because it happens approx 50 times a day, and the people asking for that are not typical H customers but typical Asian resellers with "I am going to resell it for a lot more" written on their face. Same rules as for other H shops apply to Italy.