Yes, very true. Perhaps "offshoot" was not the best word to use. That one group, however, did the kata quite differently from the way we and the way I have seen the Soke and Jiki-soke do the kata. In fact one sempai of mine was standing beside me during that particular demonstration and said to me in a whisper "zenzen chigau".
But I am just saying that they are different, and that niether of those pictures is of the Tokyo or Nagoya Yagyu Kai.