We are, as much of the world, importers from China, but many enterprises here are also, somewhat, strong exporters to China (I can see it from my dayjob as industrial automation SI), and if you factor in the small average size of Italian companies requiring many individual contacts (contrast with Germany where companies on average are bigger), you can imagine that there is a strong flow of people to and fro. Maybe the small size of companies requiring more people to establish commercial links + population being more uniformly settled across the country (no huge wildland or sparsely inhabited area left in Po Valley, except maybe some parts of Piedmont?) + a certain cultural inclination for useless quarreling hindering political action + inefficiencies in the administration + an unsolved conflict of power between central gov't and periphery possibly causing some waste of time in other quarreling + having to keep the vast group of small business owners somewhat quiet has resulted in a vast spreading of the virus.
The interesting thing is that, if you replace China with Germany in the paragraph above (wrt. the possible German origin of the outbreak in Italy), the consideration about business links would still apply.
Another interesting thing I have just noticed is that some journalists are now openly praising the Chinese handling of the crisis. Maybe this may sound strange to an American :D but there has been for some time a growing cross-partisan movement calling for stronger links to China. In fact this movement is somewhat present in European business community, so it is not so special to Italy, but nonetheless it is interesting to see these comments of open praise.