While I appreciate the optimism of some, or that some never ever saw or experienced any encounter with criminal miscreants while traveling, I don't think it's appropriate to invalidate others who simply wish to discuss the safety and theft issues honestly. Some of us have had different experiences.
The reality is that there are thieves using knives to cut open bags. I'll never forget the story of a couple who, while waiting at Roma Termini, felt that a male subject was encroaching on their space and luggage suspiciously, making them feel uncomfortable. So much so, they decided to go stand elsewhere with their thousands of dollars in camera gear. After moving, only then did they realize why the man was encroaching on their space. A slash was cut through one of their camera bags and they were about to lose a very expensive lens. As a photographer myself, I can appreciate the significance of the potential monetary loss.
I think there were some videos of similar capers uploaded to You Tube.
Pacsafe lines their bags with steel mesh to defeat thieves from slashing them open. Other products have cheap, thin plastic buckles that clip their money belt and strap together. These buckles are easily broken and can result in potential loss. The shoulder straps have steel cord in them to make them slash proof as well. If there's a better, more secure system, I'd rather use it and minimize risks. I don't think there's anything wrong with providing such information. I didn't know about Pacsafe until I saw it at Seattle REI. Then I researched it online and was impressed. On that note, I recall my wife wanting to use my slr to photograph me in front of St. Peters. I untethered it from my Pacsafe strap so she could do this. As I backed away to be photographed, a man rushed toward my wife. But I saw him watching and waiting off to my left, and got to her before he did. (What they usually do is grab the neck strap and run, taking you to the pave in the process. They do this over at Trevi Fountain and other places). Anyway, the man smirked at me, as he jogged away.
About 2 years ago now, an older gentleman was near the Duomo in Firenze, and tried the firm approach with a thief. The thief didn't respect this, and stabbed the man. Emergency surgery was conducted and the man lost a kidney. I believe this kind of assault on a traveler in Italy is rare. I guess each individual has to take stock of what action they think is appropriate as circumstances arise. Sometimes a firm "no" works fine.
I follow local news in Firenze and they have crime like everyone else, but the trends have interesting differences because they often involve gangs or individuals traveling from place to place on trains, never sticking around long enough to be apprehended. If they are, it's before they leave and sheer luck. I've spoken to various police around Italy about this, and it's a frustration for them to deal with. Same in Roma, Naples, and most everywhere else. I think small towns see less of it, at least this was our experience.
Informing yourself of these potential problems, or sharing factual information regarding it does not equate to hyper paranoid vigilance. The point is to prepare one's self with knowledge so they can avoid trouble and enjoy their travels.
The original question was "How safe are the train stations"? I shared my own observations. I also saw this at Roma Termini, but not at Santa Lucia Venezia or Lucca and others. Some may never encounter or see any thieves but it's well known and published all the same. It's the real world....all over the world.