KSR diehards will always say that and I guess it is true. But, if I practise Judo kata in my Aikido class should I tell them it's Judo, or should I call it Aikido?
That depends entirely on how you do it. If you do it with aikido principles, then it's aikido. If you do it with no aikido principles, then it's judo.
Dr. Friday's contention is simply that Kashima Shinryu kata done with aikido principles is no longer Kashima Shinryu, but rather aikido, and shouldn't be called Kashima Shinryu.
Look at it this way: Morihiro Saito's aikiken's first two kata (IIRC) are taken directly from Kashima Shinto Ryu. The aikiken taught by Michio Hikitsuchi features three kata from Yagyu Shinkage Ryu. Does this mean that Saito sensei was (or any Iwama teacher currently is) teaching Kashima Shinto Ryu? Does it mean that Hikitsuchi was teaching Yagyu Shinkage Ryu? Not at all. They kata have been altered enough by integration into aikido that those names no longer fit.