I'm not expressing an opinion either way on the accuracy of the quote from Mr. Higaonna's book, but someone certainly could question its veracity without calling anyone a liar.
To start with, we don't have statements here from Kano or Miyagi, so there's no question of calling either one of them liars. We only have what was written by Higaonno. Morio Higaonno was born in 1938, so he was certainly not a first hand witness to this conversation between Kano and Miyagi. Does the book explain exactly what his sources were in learning about the conversation between the two?
To the best of my knowledge, Mr. Higaonno is not a trained historian. He could certainly be honestly mistaken about what was said in a conversation that happened around the time he was born that he learned about second or third or fourth hand decades after the fact. Heck, even a trained historian could be mistaken about such things. Prominent martial artists make misstatements about martial arts history all the time.
BTW - I have no particular reason to doubt Mr. Higaonno's honesty, so I'm assuming that he was recounting the story as he believed it to be true. I should note, however, that prominent martial artists are no less likely to be liars than anyone else.
Personally, I would be more interested in the contents of Higaonno's series of
Traditional Karate-do: Okinawa Goju Ryu books published from 1985 through 1991, before the advent of the UFC and the increased attention given to grappling. I would assume those would give a pretty good snapshot of Goju-Ryu as it was practiced at that time, including what sort of grappling techniques were taught. I'd be particularly interested in what they show regarding ne-waza. Do you happen to have any of those books in your collection?