Quick correction: it was July 11, 1966, not 1967.
Wikipedia notes the press conference didn't actually start until 2:30; McNamara was late. CBS stuck with the newsmen discussing the issue until 2:30; ABC ran
The Newlywed Game. So you can blame McNamara. (I will say Wikipedia has no source for this, however.)
CBS had other reasons for airing the press conference. Earlier in the year, when the choice came of whether to whether to air a Senate hearing about Vietnam or an
I Love Lucy rerun, CBS's president Jack Schneider overruled the president of CBS News, Fred Friendly, and went with the
Lucy rerun, saying "housewives don't care much about Vietnam." Friendly (who had previous produced
See It Now with Edward R. Murrow) announced his intention to resign in
The New York Times, CBS accepted it, and it was a major story in that newspaper for days (which was
the news source of record at that time, as it still is). It's dealt with more thoroughly in Friendly's autobiography,
Due to Circumstances Beyond Our Control, excerpts of which can be read here:
https://books.google.com/books?id=BIpHFucuMM8C&printsec=frontcover&dq=fred+friendly+due+to+circumstances+beyond+our+control&hl=en&sa=X&ved=0ahUKEwiIvvuR-KziAhUCQawKHbMkC2MQ6AEIKjAA#v=onepage&q=fred%20friendly%20due%20to%20circumstances%20beyond%20our%20control&f=false.
Long story short, CBS brought back Richard Salant as news president and tread carefully on that sort of thing. (Schneider was not an enemy of the news department, and he and Salant got along very well.) So CBS wasn't going to skip the news conference.