Yes, of course we can. This is something that bothers me very much, because it’s influenced by the portrayal of media and, in turn, it is followed by a general attitude of stupor and (negative) surprise whenever we try to show that we have something more than that. Italy is a very varied country in many aspects and this is one of those. There’s the little Medieval village and the huge industrialized metropolis. Neither of them is out of place. They coexist
Italy is the first European producer of shoes, in 2013 we were the first producers in the world of wine (despite all the fakes), but we also have the most efficient scientific researchers - meaning that they get the best results with the, sadly, least resources, without considering all the successful Italian researchers abroad.
This report from 2011 displays some of the biggest achievements in terms of export and surplus. The Italian goods that produce the biggest surplus are, except for the usual food&wine ($6,4 billion of surplus), automations, gums and plastic ($31,6 billion), clothing and fashion ($18,1), and other products such as paper, glass and chemicals ($4,3).
Here’s some “first places” from Italy’s export in 2011, you can see everything from sunglasses to helicopters, to specialized furniture for frozen goods:
So yeah, Italy is also industrialized (though the crisis is striking really hard on many companies, small and big). We’re not stuck in the 1950s. You could meet someone who lives in a small Medieval town and find out that they work in a specialized factory.