In the early 20th century, the Japanese Karate masters sought to rewrite the Kanji of the word "Karate" from "Tang Hand" to "Empty Hand/Fist" - "Tang Hand" was in reference to the T'ang Dynasty (China circa 618AD-907AD) in which the style was originally taught. Other styles such as "Tang Soo Do" reflect the source as well.
Relevant to this fact, there is a circulating hypothesis that the originator of the martial arts as we know it originated with the greeks - during the time of Alexander the Great, Pankration ("all holds" - no holds barred) was a widely studies form or martial arts in Greece - the hypothesis states that because Alexander's empire stretched all the way to India, the soldiers practicing the style (analogous to the US soldiers "bringing back" martial arts they've trained in after the occupation of Okinawa post-WWII) might havee had an influence in India; flash forward a few centuries - Bodhidharma, the monk credited with Chan/Zen Buddhism and the Shaolin Martial Arts Style, was of Southern Indian origin of a warrior caste who traveled East to spread the wisdom of Buddhism.
And throughout the centuries, the Shaolin Temple, along with the temples of WuDang mountains (Also known as the WuTang mountains; the site of many fictionalized accountof martial arts, portrayed both on film, novels, etc. - this is where the hip-hop group Wu-Tang Clan got the inspiration for their name) were considered the central influence for the martial arts in China, and the whole of eastern Asian in a bigger context, because China was the cultural center for Eastern Asia - to reflect their importance/arrogance, the word "China" written in Chinese, means "Central/Middle Nation".
To further drive this point home, there is a pattern shared by many styles of Okinawan/Japanese Karate called "SanChin"(translated as "Three Battles" or "Three Spears", depending on style) that is also shared by, and originated from, the Fujian White Crane style, a Chinese Kung Fu style practiced in Southern China.
edit: As to the validity of the theory, it is circumstantially/logically suspect, because there are several styles, such as San Shou of China, Vajramushti of India, etc. that claim to have a history the predates their regional significance in the hypothesis. Logically speaking, it is very unlikely that any organized culture would not have an organized method of self-defense, and would have to rely on outside ideas to bring in such concepts.