If a codified system of martial instruction is not written down or shown in art then it does not leave behind any type of artifacts to indicate its existance in the past.
If a codified system of martial instruction is written down then it is by default done so within the historical period of that culture.
China has an extremely long historical period - approximately 4,000 years!
Unless there is other important related information you did not mention I would consider those conclusions little more than wild guessing rooted in a very bias view.
There are many. The practice of Shuai jiao (chinese/mongilian wrestling) is recorded in the classic rites of the Zhou dynasty (between twelth and third cenury BCE) and became a public sport around 221-207 BCE. It is still practiced today.
There are other mentions, Wikipedia has some references : http://en.wikipedia.org/wiki/Shuai_jiao#History
http://en.wikipedia.org/wiki/Bodhidharm ... connection

