Celebrities have ways of keeping stuff that would otherwise be public—marriage licenses, appearances with county clerks—pretty secret. With this couple spending a rumored $6.5 million (!) on the nuptials, you can bet that they could have a completely up-and-up Italian union on the down-low.
If that's what they wanted, which isn't likely.
In fact, it's more probable that such a celebration in Italy might be, as you suspect, more symbolic than legally binding.