Argento just released a statement, saying, "I am deeply shocked and hurt by having read news that is absolutely false. I have never had any sexual relationship with Bennett." The Bennett to which she is referring is Jimmy Bennett, whom she had visit her in a hotel room when he was 17 and she was 37.

She acknowledges Anthony paid, saying, "Anthony personally undertook to help Bennett economically." She goes on to say Bennett was litigious and made exorbitant money demands and they wanted to "no longer suffer any further intrusions in our life."

Bourdain and Argento -- who were dating for over a year before Bourdain's death -- texted each other about Jimmy Bennett, referring to him as a "donkey" and Bourdain writing that paying him is "no admission of anything, no attempt to buy a cover up, simply an offer to help an obviously tortured soul whose desperate and trying to jack you for money."

Bourdain goes on to say, "Or you just tell him to f*** himself. Either way, I am with you."

In discussing the settlement -- which ended up to reportedly be $380,000 -- Argento confesses, "I am also broke." Bourdain makes it's clear he's handling the negotiations, instructing Argento to take a call from a rep who is involved in the matter.

Asia, at one point, seems to contradict her claim she never had a sexual relationship with Bennett, saying, "It wasn't raped (sic) but I was frozen. He was on top of me. After he told me I had been his sexual fantasy since he was 12."

Asia also never addresses the photograph -- which TMZ has seen -- of Asia and Bennett shirtless and in bed with their foreheads touching. This photo was reportedly the centerpiece of their settlement.

As we reported, Argento did not want an NDA as part of the settlement since she railed on Harvey Weinstein -- whom she had accused of raping her -- for using NDAs to silence his victims.

Bourdain seemed to agree in the texts, saying, "You are not buying silence. Only freedom from inconvenience. And to help a 'poor twisted goof' get his life together."

Asia responds, "I will never buy his silence for something that isn't true since I am also broke." Yet she claims in other texts that he was the sexual aggressor.

And there's this ... at one point Argento says, "I don't fear him [Bennett]. I am no Puritan, google my ass."

As we reported, Bennett claimed Argento plied him with alcohol, performed oral sex on him, jumped on top of him and had intercourse.