Bill O’Reilly reportedly is fighting for his television life because a woman, Wendy Walsh, claims the talk show host asked her to come to his hotel room and, when she declined, he retaliated by dropping her as a regular guest on his show and reneging on an alleged promise to help her land her own show on Fox News. Walsh has not raised this claim in a court of law, nor did she complain to Fox. Rather, she made her allegations in an interview with the New York Times. They are now being investigated for Fox by the law firm of Paul, Weiss (let’s hope the firm does a better job with this one than with “Deflategate”).

Fox News and O’Reilly reportedly have settled five sex harassment claims against the host since 2002, paying $13 million in the process. I have no information about the merits of these claims.

As for Walsh’s claim, this report by Paul Fahri of the Washington Post suggests that it’s shaky.

According to Fahri, O’Reilly continued to invite Walsh on his program for four months after she resisted his alleged sexual advance. Her attorney says she continued to appear on his program because she hoped to become a paid Fox News contributor.

That’s plausible. But the issue for purposes of retaliation isn’t why she continued to appear with O’Reilly, but why O’Reilly continued to invite her to appear. If, as she says, her appearances were likely to help her, then it’s hard to see how O’Reilly was punishing her for rejecting him. Genuine retaliation likely would have consisted of sacking her, or sharply curtailing her appearances, right away.

Walsh appeared on O’Reilly’s show 13 times after the hotel incident in February 2013. He mentioned her new book four times after it was published in mid-April and repeatedly showed its cover on the air.

Moreover, according to Fahri, O’Reilly “apparently was instrumental” in securing for Walsh an appearance on “The View” during which she also promoted her book.” Walsh would later say that O’Reilly’s call to “The View’s” executive producer “really launched my book tour on a high note.”

This doesn’t sound like retaliation.

Four months after the hotel incident, O’Reilly’s producers told Walsh that her regular weekly segment would end. It has been years since I litigated a retaliation claim, but I think four months is at or beyond the limit courts typically set for inferring (for purposes of creating a rebuttable presumption of retaliation) that a defendant’s adverse action was caused by a plaintiff’s action (or, as in this case, refusal to act).

And that’s in situations where the defendant doesn’t act favorably towards the plaintiff during the intervening period. Here, according to Fahri’s account, O’Reilly took action favorable to Walsh on numerous occasions following her rejection of his alleged advances.

If the facts Fahri presents are accurate, and assuming the absence of other facts that might incriminate O’Reilly, it seems unlikely that Walsh could make out a prima facie case of retaliation based on the cancellation of her weekly segment on “The O’Reilly Factor.”

What about Walsh’s allegation that O’Reilly reneged on a promise to help her get a show? O’Reilly denies having made such a promise.

Moreover, Bunny Forrest, who appeared with Walsh regularly on O’Reilly’s show, says that when Walsh complained to her about the cancellation of their segment — suggesting that it was linked to the hotel incident — she didn’t mention a rescinded offer of a job or assistance in obtaining one. Forrest adds:

I take sexual harassment. . .very seriously. But I also believe in this instance there are some statements made in the press that aren’t consistent with my experience.

I write about Walsh’s claim disinterestedly. I’m not a fan of O’Reilly. I rarely watch his program and am indifferent as to whether he remains on the air. I take no position on his behavior in prior cases where he’s accused of sexual harassment.

My focus is solely on Walsh’s retaliation claim. It’s possible that her claim is meritorious. However, on the facts presented by Fahri (no fan of O’Reilly, as far as I can tell), her claim seems weak — much too weak to justify ending the host’s career at Fox News.