A lot of companies require automatic termination of anyone in a "personal relationship" with a subordinate.

In Letterman's case he has an employment contract that may give the network a way out. And she might not (technically) be a subordinate of his.

They're going to have to punish him in some way or it will be a big problem for them in every sexual harassment and discrimination lawsuit filed against them for years. It's those other lawsuits against the network, filed years later, that are the problem if they do nothing.