this has nothing to do with REAL danger, it's rather a warning to help your avoid tourist herds if you prefer unobtrusive exploration.
Kamyanets is a popular destination for Polish tourists, and gets extremely crowded from late spring to mid-fall, especially during weekends. so if you want to explore the city without running into several tourist groups in each site, as well as have some decent accommodation options, plan your visit off season, or at least for the middle of a week during the season.
The old part of Kamyanets Podilsky is extremely bad lit. Now, I'm not sure is this because there simply are not enough street-lights, or are they saving electricity / money. The fact is, that when it got darker, the town became kind of spooky. And as everything is in dark you can't see anything. This is no time to explore the cultural / historical heritage of this town. You can go back to your hotel or. find a nice bar in new part of town where locals hang out(the old part is even during the daylight more like a ghost-town).
Old bridge conecting Old Town and fortress, also called Turkish bridge, is very unstabil. It's supposed to only strong enough to handle pedestrians. Well, eventhough obstacles were instaled to prevent cars from driving across the bridge, they are not efficient. Cars can easyly avoid them and despite of danger keep driving over the bridge. Until the bridge gives up. Hope nobody else will be on the bridge at that time.