The martial arts legend, who died in 1973 aged 32, is a minor character played by Mike Moh in Quentin's latest movie. The star's daughter Shannon Lee has expressed anger at one scene in which he is shown boasting before picking a fight with Brad Pitt's stuntman character Cliff Booth.
According to Variety, the 56-year-old filmmaker has now defended his depiction of Bruce at a press junket in Moscow, Russia, saying, "Bruce Lee was kind of an arrogant guy."
Quentin went on to defend the scene, in which the action star is shown on the set of "The Green Hornet" TV series boasting he could defeat Muhammad Ali in a fight, before Cliff throws him into a parked car, by saying it was based on biographical research.
"The way he was talking, I didn't just make a lot of that up. I heard him say things like that, to that effect," he explained. "If people are saying, 'Well he never said he could beat up Muhammad Ali,' well yeah, he did. Not only did he say that, but his wife, Linda Lee, said that in her first biography I ever read. She absolutely said that."
Shannon criticised the way her father was "marginalised" in the movie in the same way he had been in Hollywood and Bruce's protege Dan Inosanto has taken issue with the scene, saying his mentor would never have behaved so arrogantly.
"He was never, in my opinion, cocky," Dan told Variety. "Maybe he was cocky in as far as martial arts because he was very sure of himself. He was worlds ahead of everyone else. But on a set, he's not gonna show off. Bruce Lee would have never said anything derogatory about Muhammad Ali because he worshipped the ground Muhammad Ali walked on."
The "Pulp Fiction" director also defended his decision to allow Cliff to beat Bruce in a fight as in the movie the stuntman is a "fictional character" who he meant to be a "Green Beret" who had killed a number of men in "hand-to-hand combat" in the Second World War.