I am not an expert in Roman citizenship questions, but from my experience in learning Roman history I can state that this sentence is not more than a poetic license.

The ancient world, as most of history before the industrial revolution and the building of the modern state, was a dangerous place. The city of Rome during the height of the Empire is thought to have had 1 million inhabitants. With such a high population and no street lamps during the night, the city after sunset was most probably a very dangerous place to travel around unescorted, and no common thief is going to ask if you're a citizen before stabbing you to get to your purse. The same can be said for bandits, highwaymen or pirates, or even raiding barbarians. Although it is true that the Empire was in general a safer place than any place outside of it, or after its dissolution, the crime rates during those times would be way way higher than they are nowadays in any developed country.

It is true though that Roman citizenship carried some mystique of protection during those years (Late Republic, Early Empire), but this again only really matter if you were a wealthy citizen or if there was a big number of citizens who were harmed, and specially in foreign lands. If a dirt poor citizen were murdered by bandits, the State wasn't going to bother much hunting them. But when wealthy Romans were captured by pirates, they were held for ransom, knowing that they would be paid for. The First Mithridatic War officially started after the Asiatic Vespers, in which Roman and Italian citizens were systematically murdered in different towns around Asia Minor. The incident provoked an out-roar and the definitive intervention of the Legions in the area.