It seems even more unlikely, given that China has had so much interaction with the nomad peoples from Mongolia, Manchuria, and central Asia, who lived mostly off of their herds and milk-products.
Dairy products never really made it into Chinese diet.
The next question to ask is why diary products didn't make it into Chinese diet despite the interactions with the nomad peoples :)
I still find it interesting, since many of the more successful Chinese ruling dynasties have central/north asian roots (Tang, Yuan, Qing). Considering that Genghis Khan is probably an ancestor to most of the eastern half of eurasia, once might expect those lactose-tolerant genes to be more prevalent.
This is simply wrong.
Maybe some 16 million. But that has also been more of a hypothesis. See http://clubtroppo.com.au/2012/10/15/why-genghis-khan-wont-ha... for one of the refutations for instance.
I do this not to participate in the argument but to point uninvolved readers to objective sources.
Chinese and Altaic people are not related. See http://en.wikipedia.org/wiki/Altaic_languages
By Altaic I mean Central Asians like Mongolians and Turks/Turkic.
When equating "people" with the language they speak, something that was very popular in the 18th & 19th centuries[0], it is important to remember that the ancestors of many people you know today probably spoke a different language 200 years ago.
[0] For a good historical summary, see http://www.ucpress.edu/book.php?isbn=9780520244559