This is a very interesting subject! Italians, especially those who speak dialects from the north of Italy, often claim to be able to understand quite a lot of Spanish if it's spoken slowly. (They also claim there's quite a bit of mutual compatibility between Northern Italian dialects and Catalan, another Romance language spoken in Spain.)
Of course, I don't for a second doubt your friend's reporting. Languages are hard!
The weird thing is, that Spanish speakers tend to report that they have a much more difficult time understanding Italian than Italians have understanding Spanish.
Linguists call this phenomenon asymmetric compatibility, and you run into it with other language groups too, where mutual comprehension (limited or not so limited) doesn't flow equally in both directions.
Sometimes (like with Italian dialects themselves) this is about education. Everyone in Italy learns standard Italian in school, and since standard Italian is based on certain dialects, people in the rest of Italy don't have a lot of problems understanding those dialects.
But can somebody in the Veneto communicate with somebody in Naples if they each speak their hearth language? Not so much!
You see the same sort of artificial asymmetric compatibility between Ukrainian and Russian, for example. You'd be hard pressed to find a Ukrainian who couldn't understand most of what a Russian speaker said if he really had to. But finding a Russian who can understand spoken Ukrainian is a far more rare occurrence, even though the languages are very closely related.
This is also down to education. Until recently, all Ukrainians studied Russian in school.
There are more natural examples of asymmetric compatibility, such as between Icelandic and Danish, and it's quite a fascinating subject, really.
Sorry for the ramble, and thanks for the interesting story!