uhm. I think you should probably look up some info about this.
Yes, athletes from other countries train in the US. US athletes also train in other countries.
But look at the top medal producing countries and you'll realize all the sports that those countries do the best in are sports that those athletes train at home in. Speed skating in the Netherlands, cross country skiing in Norway, hockey in Canada (this is a bit convoluted at the higher levels).
It's the countries that don't do well that don't have the proper facilities in their own countries that are the ones who primarily train in the US and other countries.
Also there are many many US athletes in skiing, boarding, hockey, and skating, etc who train in Canada at places like the Whistler during the summer or at the Calgary speed skating rink etc.
They're really not products of US sports. They go where the facilities are, and the US, having hosted more than one winter Olympics and being fairly easy to go to and train in, is a top destination simply because of the facilities.
Also what are you saying about being in the education system? Not understanding that.