Yes, and keep those kids in that training environment, and their kids, and their kids, etc. for about 20,000 years. Then those decedents might be of similar talent to their East African counterparts.
Here's why genetics are impossible to ignore in the case of East African dominance in distance runner. First, there's more genetic variety in Africa. The human species originated in Africa (specifically East Africa) and a portion of that original population went on to populate the rest of the world, so the entire rest of the world is operating on a fraction of the original human population genes. This is why there's greater genetic variation between Africans of different linguistic groups that there are between Europeans and Asians.
After that, the people that live in the Rift Valley and highlands of Ethiopia have lived there for tens of thousands of years. Tens of thousands of years at high altitude has led to evolutionary adaptations to low oxygen environments, and the fact that running has been a vital means of personal transport and managing livestock during humanity's history there, means that people got very good at running at high altitude or weren't likely to have significant numbers of offspring.
The end result is what we have now: East Africans with a predisposition towards long distance running. You tell me how Ethiopians live and work comfortably at 4000m above sea level with virtually the same hemoglobin count as someone from sea level? It's not will or desire; the conditions of the environment have shaped the gene pool:
http://icb.oxfordjournals.org/content/46/1/18.fullHow is what you're suggesting different than someone saying, "people of African decent aren't more resistant sunburn because of their genes, the conditions of their lives have made them tougher."