It could be the Last Bastion of true Wizard Dueling where it is not against the law for the duel to result in the death of one or both participants if it is a matter of honor

It could also be a place where the Death eaters who escaped the Ministry ran because there is no extradition
Oh and even though those escapees might be powerful and scary in their more civilized lands in Italy they must be careful who they offend because of the extended blood lines and the code of Vendetta which is still practiced there.
The distinction between Pure and Muggle is blurred by the intensive attention to family trees in Italy, a muggle born might be able to be tracked back 1,00 plus years to and old and still existing family of powerful wizards and witches. This means harming someone who is a muggle might still bring down upon the offender the wrath of some family that will see their punishment as a matter of honor
To have Vendetta declared on your person means that till the code is satisfied there is no safe haven even in the lands of the ministry or the new world