Well, firstly, to make athletic talent visible, all kids need to be more balanced towards sports than specialized into academics. That reduces the academic momentum of the country. Secondly, those two talent pools do indeed overlap. Nothing says you need to be stupid to have good muscles. There are people with average or even slightly below average intellect and fantastic athletic talent but would prefer to spec into a normal office job rather than take the risk of being a professional athlete. That is a cultural and risk management decision.
Lastly, not as a reply to what you wrote but as an addendum to what I wrote:
Take America's Medals Away.
While Chinese athletes might not always overlap in talent with their American counterparts, plenty of poor countries do. Specifically, in running, Kenyans and Ethiopians are excellent at the marathon and Jamaicans, Bahamans, etc... are excellent at the dash. The problem is that these countries are often without the funds for proper talent recruitment and training, lacking training sites, equipment, and advanced sport science knowledge. China has all 3. China should invest in building "Friendship Arenas" in these countries with scholarships for the local talented where Chinese sport scientists go to help train them with what we know to give them a further boost to winning their running races. We can even send Chinese athletes to train with them to see if there is anything we can learn. These gold medals won't belong to China, but making the US lose them is just as good. We've already seen from this Olympics that without a rush of running medals, it takes a lot of luck for the US to compete with China in gold medals.