Douglas believes the alleged incident "derailed any future career I would have had at CBS." Late Saturday, she added: "Real change will occur when I can walk through the front doors of CBS and resume the creative relationship that was so tragically cut short."
The New Yorker story goes on to allege that six former CBS employees said Fager would get drunk at company parties and "touch employees in ways that made them uncomfortable."
Fager denied the allegations, telling the New Yorker "they never happened."
On Sunday, Ronan Farrow, the author of the New Yorker story said he spent eight months vetting the women's accounts.
"These are women who began coming to me immediately after the Harvey Weinstein story," Farrow told CNN. "We have vetted and re-vetted these sources and my honest impression is that these stories are not only true, but also not fueled by any kind of opposition research."
CBS News has hired a law firm to conduct a separate investigation into claims of misconduct, which it says will include the allegations in the New Yorker article.
Moonves says he has always abided by the principle that "no means no" and he denies ever misusing his position to harm anyone's career.
Fager, for his part, called it "wrong that our culture can be falsely defined by a few people with an axe to grind."
The story comes at a time when CBS is in a legal battle with Viacom. Shari Redstone is a major shareholder of both media companies, and has been seeking to combine them.
CBS owns the CBS TV network, cable network Showtime and the publisher Simon & Schuster. Viacom controls several major cable networks, including Comedy Central, MTV and BET, and movie studio Paramount.
Moonves has fought the merger.
"The timing of this report comes in the midst of the Company's very public legal dispute," a statement from CBS' independent directors said Friday. "While that litigation process continues, the CBS management team has the full support of the independent board members. Along with that team, we will continue to focus on creating value for our shareowners."
Ms. Redstone issued a statement Friday supporting an investigation into the allegations against Moonves and countering any claims that she played a role in the report: "The malicious insinuation that Ms. Redstone is somehow behind the allegations of inappropriate personal behavior by Mr. Moonves or today's reports is false and self-serving. Ms. Redstone hopes that the investigation of these allegations is thorough, open and transparent."