Part of this is cultural. Okinawan had its own indigenous art of grappling called "te-gumi" which most would have participated in. An equivalent would be how in many places in the US wrestling is taught from early childhood in school/community programs. The idea of "ne-waza" really didn't exist except as a subset of some Japanese Jujitsu, but wouldn't have been widely taught until Jigaro Kano added it to his Judo.
Karate as we know it was originally a civilian self-defense system that addressed the most common attacks of the time (Patrick McCarthy refers to this as the "Habitual Acts of Violence"). The grappling contained within the Okinwan karate would have been grabs, holds, throws etc. and some groundfighting, but not ground grappling like we see in BJJ. All of the karate masters would have been trained in these applications, both applying and defending. If you look at the Bubishi (referred to as the bible of karate) you can see various grappling methods included, such as, single leg takedowns. Here is a blog that highlights some of this based on the Bubishi:
48 techniques (part I)
I don't agree with Jesse that ALL of Okinawa had no karate styles in that the karate from Naha was very different from the karate from the Shuri and Tomari regions due to body mechanics. Shuri/Tomari methods became Shorin-ryu and the Naha method became Goju/Uechi ryu. That doesn't mean that students didn't learn from the various areas and incorporate some ideas, but the way that Jesse explains his viewpoint makes it sound like "all karate was the same before style labels", which was not the case.
But, I agree with Jesse that ALL styles of karate are fake, as are all styles of martial arts. By that, they were all created at some point by somebody and passed on by another bunch of somebodies. Okinawan karate was also much "looser" than the Japanese version. A teacher would have various versions of the same kata that would be practiced and training was done one to one with a student and the kata would vary between students. Once labels did come into play, this is where you started to see the argument of who learned "the real art" or which version was more authentic. Also, as an instructor refined their own art, it would have been different at different times. The Japanese were really the ones responsible for "freezing things in time" and not changing things.