What's behind the teen prodigies inventing things?
I actually disagree with the answer given, and having judged a fair number of high-end science fairs myself (not Intel, granted, but the all-Chicago science fair, which is essentially an Intel qualifier), took something different away from it. I am also close friends with a number of Intel finalists, and have discussed their experiences in depth. 

While most of the high schoolers at this level of science fair are extremely intelligent and will eventually become great, independent drivers of research, at this level they typically are not there yet. Their projects, for the most part, are designed by a faculty member or senior grad student/post doc, and the student is guided through the many experimental steps involved until they find something, at which case, because the research was done in a university lab and it is already better than 98% of other science fair projects (which are usually done at home with minimal resources), they typically do very well in science fairs. 

Occasionally, one of the students is truly head and shoulders above everyone else, and can operate somewhat autonomously in a lab setting and can ask and answer their own questions - essentially at the level of an older graduate student. But, like a graduate student, they typically still need the oversight of a senior person who "gets" research. 

I realize that this response is mostly to the answer given above, and not the the main question, but I felt strongly that the answer needed to be addressed. 

As for prodigies: 


In the sciences, which require tons of background knowledge to even know what's going on (see: cancer), I have never, ever, heard of a true prodigy who could, for example, be running a 15 person cancer research lab, writing papers, etc. You don't just "understand" cancer the way some people "understand" math, innately. 
In math, the story is much different. There are always math prodigies, and they typically get tenure in their early twenties (see: Manjul Bhargava, Charles Fefferman, etc.)
There are, of course, CS "prodigies" who are good at coding and creative enough to think of something that hasn't been done. But this isn't really what you are talking about. 


tl;dr: there are no true "prodigies" in science. There are in math, though.