Like that.
The wife was an employee, too, and their relationship was long-standing, or off and on for a period of time. You don't think she knew about his extracurricular activities with other staff members before the marriage? As I understand it, the relationship with the woman who was involved with the extortionist ended with the birth of his son, which in turn pre-dated the marriage ceremony with the mother of his son. So ... my strong suspicion is that Dave hasn't been sleeping on the couch since he told his wife about the extortion attempt. I don't think any of it was news to her.
The threat was more about his public image - which ties back into the possibility that some of these affairs weren't consensual. If CBS decided to fire him, then his world would come crashing down around him.
Private affairs turned public take on a whole 'nother level of "weightiness". What's between a handful of people is often easier to deal with than when the whole world is on it 24/7.
Which i not to eliminate the possibility of something insidious like a "forced" relationship. But I can also see where having a private affair turned public could also be viewed as causing one's world to come "crashing down". Quite easily, in fact.