Perhaps, but it might make sense to travel ten light years to acquire resources. You might not even send people out to collect them. Perhaps you send out robotic missions that send the materials back here. If you had the technology to accelerate to ten percent of the speed of light, you would begin receiving resources within a century ( I'm assuming travel to our nearest neighbour here, 4ish ly away).
Over the past century, our population and our dominion over this planet have grown exponentially. As we deplete the resources on Earth and as technology advances, there will come a point where exploiting the materials in the rest of the solar system will be as profitable as exploiting the remaining resources on earth. If our growth continues as it has in the past, we would consume the resources in the rest of the solar system relatively quickly, and get to the point where exploiting the resources in the next star system over is as profitable as those remaining in the solar system.
Relative to the current age of the galaxy, it wouldn't take long for a species like ours to spread across the galaxy. The Independence Day reference was tongue in cheek, although if you've traveled across ten light years to get something your species needs, maybe you're less inclined to share!
I believe that given our insistence on perpetual growth, our curiosity, and there always being a few individuals willing to take great risks, we will eventually try to leave our home. Why not others?
But that is the paradox I guess. Obviously there is something wrong with this scenario. There are so many possibilities to explain it too, that it's a lot of fun to speculate. We won't know for sure until we expand and/or meet our neighbours, find we can't or shouldn't expand at all, or occupy an otherwise empty galaxy. I just hope I live long enough to see the first interstellar probes start sending back data.
(and the Voyagers don't count... I want pictures from the next system over!)