"I say this as someone who is such an admirer of his work," she said. "His process was not conducive to the ethos that I demand in my productions. He has a process that, in some ways, seems to require a combative energy, and I don't personally believe that is conducive to the best performances."
Wilde continued, "I believe that creating a safe, trusting environment is the best way to get people to do their best work. Ultimately, my responsibility is to the production and to the cast to protect them. That was my job."
In an email to Variety on Thursday, 36-year-old LaBeouf (whose rep previously declined to comment for the cover story) responded to Wilde's comment, claiming he actually "quit the film due to lack of rehearsal time."
He also provided to the magazine an email he said he sent to Wilde this week in response to the article. Variety published the full email, in which the actor wrote to Wilde, "You and I both know the reasons for my exit. I quit your film because your actors and I couldn't find time to rehearse."
While he said he was "greatly honored" by Wilde's praise of his work, he said he was "a little confused about the narrative that I was fired."
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According to Variety, LaBeouf also provided past text messages and a video that Wilde allegedly sent the actor two days after he said he quit the film in August 2020, asking him not to go.
"I feel like I'm not ready to give up on this yet, and I too am heartbroken and I want to figure this out," Wilde said in the video, according to Variety. "You know, I think this might be a bit of a wake-up call for Miss Flo, and I want to know if you're open to giving this a shot with me, with us. If she really commits, if she really puts her mind and heart into it at this point and if you guys can make peace — and I respect your point of view, I respect hers — but if you guys can do it, what do you think? Is there hope? Will you let me know?"
A rep for Wilde did not immediately respond to PEOPLE's request for comment.
In his email, LaBeouf began by telling Wilde that he prayed for her and her family, and shared personal details about his recovery in the past year and becoming a father. He then segued into a plea for Wilde to set the record straight.
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"I know that you are beginning your press run for DWD and that the news of my firing is attractive clickbait, as I am still persona-non-grata and may remain as such for the rest of my life," he wrote. "But, speaking of my daughter, I often think about the news articles she will read when she is literate. And though I owe, and will owe for the rest of my life, I only owe for my actions."
He concluded the email: "Firing me never took place, Olivia. And while I fully understand the attractiveness of pushing that story because of the current social landscape, the social currency that brings. It is not the truth. So I am humbly asking, as a person with an eye toward making things right, that you correct the narrative as best you can. I hope none of this negatively effects [sic] you, and that your film is successful in all the ways you want it to be."