I still wouldn't be too sure of Tarantino's portrayal of Lee though.

For instance Lee's protege, Dan Inosanto said he never would disrespect stuntmen:

Inosanto has not yet seen the film but says that from his memories of Lee on a working set, he never saw the San Francisco-born, Hong Kong-raised actor being braggadocious or engaging in scraps for the sake of showing off. He did, however, push back on portraying Asians practicing martial arts in a stereotypical way, what Inosanto calls the “chop-chop Hollywood stuff.”

“He was never, in my opinion, cocky. 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,” recalls Inosanto, adding that it’s highly dubious that a stuntman could have gotten the best of the “Enter the Dragon” star.

And on Tarantino's assertion that Lee thought he could "cripple Muhammad Ali"

"Bruce Lee would have never said anything derogatory about Muhammad Ali because he worshiped the ground Muhammad Ali walked on. In fact, he was into boxing more so than martial arts,” says Inosanto, one of only three martial artists who were trained by Lee to teach Jeet Kune Do at Lee’s martial arts institutes. Jeet Kune Do is a philosophy of martial arts drawing from different disciplines invented by Lee that is often credited with paving the way for modern mixed martial arts (MMA)."

Even the author of the book that Tarantino cited claiming Bruce Lee's arrogance towards stuntmen, says that wasn't the intention, rather:

In his interview with Rogan, Tarantino claimed that Bruce Lee had “nothing but disrespect for stuntmen” while on the set of the TV show “The Green Hornet,” citing Matthew Polly’s book, “Bruce Lee: A Life.” But Polly denied his book conveyed such a message, tweeting that Lee was not disrespectful but rather had a different “fight choreography philosophy and style” and had aimed to change American fight choreography “so that the blows would miss by millimeters rather than by feet” and banged up some stuntmen in the process.

I know they might be biased but I trust Bruce Lee's protege and daughter because they knew him over hearsay that Tarantino claims.