whether you want to call it a first-world problem or not, a problem is a problem. You see stress does not care about the country you live in or the wealth you have, it will effect everybody. Problems are relative to one's life. What seems like a minor problem to one person could be a major problem for another.
Problems may also be relative to the area, or a more specific connection like a community or culture. Social stress is a huge problem even in First-world countries. These little annoyances can build up to be huge problems for ANYONE. whether they came from a tough place or not, these problems could get to anyone.
Now it also depends on what type of problem we're really talking about here. Say for instance, a child didn't get the game he wanted for Christmas so he throws a fit. Okay, that's a minor problem, it will blow over and that's that. But if the problem didn't cause much trouble than it's just a minor problem to begin with. That same kid could still have other problems that are significant to them and their life. Say maybe that kid gets beat up in school for the way he dresses. Sounds stupid, what a strange problem to occur because of fashion, but not that uncommon. The smallest trivial things can cause problems and what ever your social class, you'll always have stress to deal with.
A better example might be a rich man complaining about the difficulties of finding a good driver. May sound stupid to us non-rich people who have to walk, take the bus, or drive ourselves around but if WE we in that position, we might agree, it's an annoying problem that would effect our daily lives. Of course, still a minor problem and im sure even the rich man would agree with that. Point being, our problems aren't all that different, the minor things continue to be minor and the major may take different shapes but are still big problems that would effect any body in that position.
even after 3 paragraphs i dont feel like i explained myself well enough... oh well.