Bruce Lee's daughter and Matthew Polly, who wrote the gongfu king's biography, are not happy with Quentin Tarantino.
Lee is featured in Tarantino's movie Once Upon A Time In Hollywood, with Brad Pitt's stuntman character Cliff Booth having fight scenes with actor Mike Moh who portrays Lee.
Lee's fans have lambasted the director for painting Lee as an arrogant person, with Moh's character saying he could beat boxer Muhammad Ali.
But Tarantino, who was promoting the movie in Moscow, fought back, saying he was not making things up.
"Bruce Lee was kind of an arrogant guy. 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. 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."
In July, Lee's daughter Shannon told trade publication Variety that he was "continuously marginalised and treated like kind of a nuisance of a human being by white Hollywood, which is how he's treated in the film by Quentin Tarantino".
Lee's training partner Dan Inosanto told Variety that Lee was perhaps "cocky" when it came to martial arts "because he was worlds ahead of everyone else".
But Lee would have "never said anything derogatory about Muhammad Ali because he worshipped the ground Muhammad Ali walked on".
Polly, author of Bruce Lee: A Life, told USA Today that the action hero was "often a cocky, strutting braggart, but Tarantino took those traits and exaggerated them to the point of caricature".
Lee's fans are also upset over scenes in Once Upon A Time where the icon cannot hold his own against Pitt's character.
Tarantino punched back, saying: "Could Cliff beat up Bruce Lee? Brad Pitt would not be able to beat up Bruce Lee, but Cliff maybe could. It's a fictional character. If I say Cliff can beat Bruce Lee up, he's a fictional character so he could beat Bruce Lee up."
Moh himself said in another interview that he was at first concerned when he read the script.
But he bought Tarantino's point that the fight scene between Lee and Booth was needed to prove how dangerous Booth is.
Moh clarified that Lee did not lose the fight - he took the first round and lost the second.
The face-off was broken up before a winner could be determined in a third round.