There are going to be huge differences between how Rick travels and how the rest of us travelling independently travel. In fact, the irony is that his travel style mimics travel on one of his organized tours much more than it does independent travel.
First, like every other television travel-show host, Rick does not travel solo or just with an American friend or family member. He travels with a crew.
Second, the presence of a film crew with a camera rolling automatically means that any interaction captured on film will be staged rather than fully authentic.
Third--and most important--Rick is usually accompanied by local tour guides whom he uses in his tours or at least recommends in his books. And certainly for the most part, his trips are exhaustively planned. We don't see Rick on his own calling a Paris restaurant for reservations or showing up at a Paris restaurant asking for a table or sitting alone trying to deal with a challenging Parisian waiter. We don't see him in a huge train station constantly scanning the station's train monitor to see what his gate his train leaving in 20 or 15 minutes will be boarding at.
He may visit the same museums he recommends, and stay in the hotels and eat in the restaurants he recommends. But wherever he goes, with his visibility and camera crew in tow, he is like an influential food critic who is recognized immediately as soon as he steps in a restaurant.
His shows have inspired a generation of Americans to travel to Europe. But his philosophy is simply that you can travel to Europe on your own (though he has tours for one wanting a tour), that you don't need to stay in expensive hotels to have a great time, and that interacting with people in the foreign countries we visit can be educational and rewarding, though this means for most of us a venue in the UK or Ireland or by happenstance the proximity of those who speak English well.