There's some truth to that statement. One of the best pieces of advice I got was from a college professor whose course I took in high school: "You're headed for great places. Don't sacrifice your childhood/youth just to get there faster."
At the time, I didn't really appreciate the advice, but looking back, it gets truer every day. Take some time to appreciate the little things.
The quote aneesh's professor gave reminds me of the "This too shall pass" parable. That story is as powerful as any I've ever read. I bet that there's not a day goes by that I don't find myself saying "This too shall pass": http://en.wikipedia.org/wiki/This_too_shall_pass
This is why it feels empty. Because although you did something a few years earlier than other people, lots and lots of other people already did it, are doing it, and will be doing it soon.
The rat race is one of relative achievement. One can pile on all the plaudits and laurels in the world and it still comes down to jumping through other people's hoops for approval.
The only thing that doesn't feel fake is absolute achievement -- when you do something new, regardless of age, and regardless of media coverage or getting puppy snacks from the outstretched palms of condescending adults.
Obviously, it's good to strive for creativity and novelty in your work, but you also have to maintain a sense of perspective: if you've set your goals so high that your definition of "achievement" is isomorphic to "originality", then you're probably in for a lifetime of disappointment. It's a hard problem to be original -- there are a lot of other people in the world, and most of them are trying to be original, too. In fact, being original is a lot like being famous, because you can strive for it, but your success is largely determined by what other people do; it's probably bad to condition your self-esteem on the actions of other people.
For what it's worth, here's my half-formed philosophy: you have to do whatever it is that gives you a sense of personal satisfaction and contentment. Your accomplishments don't have to be great; they don't have to be original; they don't have to make you famous. As long as you can look in the mirror in the morning and feel excitement about the day, you're doing pretty well.
Perhaps I should have described another trap. It is too easy to grow up with the sense that one should work on only grand things.
"The worthwhile problems are the ones you can really solve or help solve, the ones you can really contribute something to. [...] No problem is too small or too trivial if we can really do something about it."