In another thread I wrote:
For me, what was hard to believe was that Christopher Tolkien 'disowned' his own son over films based on The Lord of the Rings -- according to a news article that was later publicly corrected by Christopher Tolkien, and Simon Tolkien as well.
I would like to correct this statement after listening again to the interview in question with Simon Tolkien. In an interview of 13 April 2010 -- Simon Tolkien: The Inheritance, Diane Rehm, NPR -- Simon was asked about a 'dispute' concerning the Estate (at first Mr Tolkien made Diane Rehm repeat her question, saying that he didn't understand it):
Diane Rehm: '(...) your father's and your grandfather's estate. Was there a dispute?
Simon Tolkien: 'No, none at all. There was a subsequent problem that I had, ah, back when the movies were coming, we had a bit of a falling out with my father that's now composed, but the actual inheritance from my grandfather, who died in 1973, on to my father as literary executor I think was entirely smooth, and what my father has done since 1973... (...) We had as I say a falling out...'
By the way this was an audio interview, so obviously the written form here is mine. In my opinion Simon Tolkien put an emphasis on 'I had' but in any case the interview can still be found on the web, is 51 minutes 34 seconds long, and the question above can be found at around 28:32 in.
So it seems that Simon's 'No, none at all' was rather in reference to the matter of JRRT's inheritance, and the dispute with his father Christopher is a different matter, here characterized as a bit of a 'falling out' at the time the films came out.