I don't think that is entirely correct. The KL1 will FIT on a L1 body. It should have the same threads. The issue comes from the fact that the L1 body contains the electronics and the L1 head is dumb (just has the emitter wired to the contacts). So if you have a L1 body connected to a KL1, it will try to supply the voltage the KL1 needs (which is 2.4-9.0V??) because it is expecting to supply the Vf of the LED.
So it would probably work, but might harm something. I don't have a L1 to try it with, and don't know if I would do it if I had one. Now, if you had a L1 body, and a stripped out KL1 head with no electronics (which I happen to have
) it should work fine.
I keep considering getting an old L1, but don't really have a need for it so I haven't done it yet.
schiesz