I have a friend who recently visited Japan, and he found that Japanese citizens were simply fascinated by his American-ness. I'm sure you've heard of this phenomenon elsewhere, too; because American culture is so prevalent, people living in non-American countries will take a great interest in American people who travel abroad.
Would this hold true during the glory days of the Roman Empire? Would the average Roman citizen, traveling abroad, be well-regarded because he comes from a nation with an expansive culture that no doubt transcended local geography?
I know the answer is probably somewhere around "it depends", but would it depend on?
Edit: I suppose that the "average" Roman probably wouldn't have enough denarii to travel abroad. So maybe we're talking about the Romans that aren't filthy upper-crust rich but still well-off enough to make the occasional trip outside of the Empire?
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.
Honestly, they were being polite. Its really common for us Americans to assume people are fascinated by us simply because we exist but that is not the case, ok? They would have been just as interested in a Swede, Spaniard, Dane, Englishman, Brazilian, etc. It is the novelty of some one new. Japan is one of the most homogoneous populations on Earth; anyone outside the norm is notable.