Full quote: "Did you know that two thousand years ago a Roman citizen could walk across the face of the known world free of the fear of molestation? He could walk across the Earth unharmed, cloaked only in the protection of the words civis Romanus -- I am a Roman citizen. So great was the retribution of Rome, universally understood as certain, should any harm befall even one of its citizens."
I replied to a similar question earlier. I am sorry to paste a previous answer, but it addresses your inquiry.
I think it is important to consider the nature of Roman citizenship.
"But no one who had any acquaintance with our laws or our customs, who wished to retain his rights as a citizen of Rome, ever dedicated himself to another city." - Cicero Pro Balbo
The Apostle Paul was a Roman citizen in the first century. It is important to remember that while Rome was involved in the region via Pompey the Great annexing it in 65 B.C, it did not become a Roman province until 6 A.D.
Paul's citizenship carried with it some very specific immunities and privileges. For instance, no Roman citizen was legally allowed death by crucifixion. Paul was taken into custody for disturbing the peace when a number of Jews were unhappy with his proclamation of a new sect that claimed Christ as the Messiah. The instance is recored in Acts 22 and addresses your question:
The tribune directed that he was to be brought into the barracks, and ordered him to be examined by flogging, to find out the reason for this outcry against him. 25But when they had tied him up with thongs, Paul said to the centurion who was standing by, ‘Is it legal for you to flog a Roman citizen who is uncondemned?’ 26When the centurion heard that, he went to the tribune and said to him, ‘What are you about to do? This man is a Roman citizen.’ 27The tribune came and asked Paul, ‘Tell me, are you a Roman citizen?’ And he said, ‘Yes.’ 28The tribune answered, ‘It cost me a large sum of money to get my citizenship.’ Paul said, ‘But I was born a citizen.’ 29Immediately those who were about to examine him drew back from him; and the tribune also was afraid, for he realized that Paul was a Roman citizen and that he had bound him.
Also when thinking about your question you should consider the Constitutio Antoniniana of Caracalla in 212A.D. This extended citizenship to all free-men in the Empire. It is an important detail that there were varying tiers of citizenship. There is much debate about the extent to which this granted a legitimate citizenship and the extent to which the measure contributed to the "Crisis of the Third Century".
A relevant and available article on Paul's citizenship is "Paul the Roman Citizen: Roman Citizenship in the Ancient World and its Importance for Understanding Acts 22:22–29" by Sean Adams.
I think an easier question to answer might be "How certain and how severe was the retribution of Rome, should any harm befall one of its citizens?"
At least, this is an aspect of the question which hasn't really been addressed (/u/MarcusDohrelius touches on it obliquely), and I think it forms the basis of the answer to the larger question. Basically, if you harmed a Roman citizen anywhere in the Empire or out of it, were you likely to be punished for it (and therefore be deterred from such an action)? Are there notable examples of this?
