This is true. The strategy employed in karate favors striking, dumping a person at high velocity and/or breaking something in the air or after they hit the ground. However, it should be noted that many of the old masters who practiced pre-1920 also had experience in grappling. Okinawan wrestling, or tegumi, was quite common throughout the islands and it was common for young people to challenge each other to matches. In fact, from the materials that I've read, it was more common for two people to employ tegumi in a match against each other than karate because tegumi was more suited for those types of matches. Karate was considered for life protection only.
It seems obvious to me that there was some crossovers. It seems obvious to me that if a fight ended up on the ground, a well rounded practicioner could apply karate principles and mix them freely with grappling. This is one of the reasons why I tend to teach more of it in my dojo. Of course my background is in judo and jujutsu, not tegumi, so I kind of go with with what I know. In principle, I think this probably matches up more with how the old karateka practiced. From my research, I'm fairly certain that there was a separation between the strategies employed with tegumi and karate. I'm not sure how strict that separation was though. Was it so strict that kata could only be interpreted standing up? I certainly don't know enough to make that judgement, so I won't rule out the grappling interpretations.