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In his 2008 book "X-Films", Cox expands on this incident to say that he wanted to fire Stanton and re-work the script so that the final scenes revolved around Lite. "I felt Sy was doing better work than Harry. His character had started out with almost no lines: Sy had created Lite from the ground up." In this telling of it, the producer, Nesmith, turned the plan down. Although I have not yet had a chance to review it, I'm told that the roundtable discussion on the Blu-Ray disk (2012) has Cox stating that he actually did write Stanton out of the film. The "Shots in the dark" scene is given as an example.
Lite only has 3 significant scenes with him and Otto riding around. The first scene, with the rat, could easily be one that was switched from Bud to Lite. The last scene is the one mentioned by Cox. The middle scene, however, seems to have been written specificially for Lite since it contains Lite's monologue. Cox's comments in "X-Films" would suggest that this scene had already been at least partially created prior to this incident, since he is clearly saying that Lite's role had already been significantly expanded. This also raises the possibility that the scenes given to Lite had more to do with Cox's appreciation of Richardson than his dislike of Stanton, although it may certainly have been a combination of the two.
It may or may not be significant that none of Lite's 3 scenes take place before the scene with the baseball bat. They wouldn't have been shooting in chronological order, of course, but when Cox says "final scenes" there is no way of knowing if he meant the scenes which hadn't been filmed yet or the ones which would appear after the one with the bat. And as a final caution, we should remember that Hollywood memories recalled 30 years after the fact might be prone to exaggeration or distortion. So in the end, you have to decide for yourself what the real answer to this question is.