The answer is that both of her ideas were right. Some styles came from other styles. Others began on their own.
The coining of the term Karate even has an example of this. Te was the original martial art of Okinawa. Depending on what city you lived closest to you would either do Shuri-Te (from Shuri city) or Naha-Te (from Naha city). After Kung-Fu had influenced Te, the term Karate was coined. Kara originally meant Chinese, although when Okinawa became part of Japan they changed the meaning to "empty" (kara meant both words since they are homophones).
Other styles have even cropped up out of Shorin-Ryu. Shotokan, a very popular style of Japanese Karate was actually invented by an Okinawan Shorin-Ryu master Gichin Funakoshi. When he traveled to mainland Japan to teach Karate at Universities, he altered Shorin-Ryu into what would eventually become Shotokan. This is the reason that both styles have many of the same kata but they are done slightly differently.