You may well be right.
Later this morning, the phones will be screaming between the affiliates and net. Even the O&Os (Owned and operated stations in major markets such as WCBS in NY; WLS,Chicago; KABC,LA) will chime in, saying advertisers are screaming.
Imagine you are the GM of the CBS affiliate in Dallas. How loud do you yell?
I'd inform NY that you are dropping the CBS Nightly News beginning next Monday, if Rather is still in the anchor chair. A few major affiliates send that message, and Rather will be G-O-N-E.