You're almost correct... actually families in China send their kids at a very young age (3-4 yrs old) to training camps where the trainers will place them where they think they will do best regardless of what they personally want to choose to do sports wise...
They will then keep developing them as they grow and pick out the ones with the most potential to compete, the ones that don't show much potential in the areas they are placed sometimes get to pick a sport they want to do...
Like i think the Chinese girl who won the gold medal for swimming was originally trained to by a gymnast, and even the Chinese huddler was originally trained to do another type of track and field i think if memory serves me...
