Contrary to some recollections, I am pretty confident that none of the broadcast networks carried the actual launch live, at least not in the Eastern and Central time zones -- only CNN did. (It is possible that it was carried live on the West Coast since the launch would have taken place during the PST broadcast of "Today" and GMA.) There may well have been some individual stations that pre-empted their normal programming and carried it via CNN, particularly in markets with ties to the space program or to that specific flight (I'm sure WMUR-TV in New Hampshire was covering it live because of Christa McAuliffe). Those who saw it in school or elsewhere probably were watching CNN (if their school was cabled) or one of these local opt-out stations. It is true that KNBC in L.A. covered it -- that is the source of the clip often repeated in tributes with the audio of the KNBC guy (NOT NBC's Tom Brokaw, though they had similar timbre voices) exclaiming, "My god....there's been an explosion." Of course, the broadcast networks cut in very shortly after the accident. Though, as I related once before on this board, CBS was a little slow coming up -- I was in Jacksonville at the time, and the local CBS affiliate (WJXT) had to use CNN coverage of the tragedy for a while until CBS went live with the story.
Of course, many probably THINK they saw it live in retrospect because only minutes later everyone was showing tape of the launch and accident, and with the short delay and live look of tape, the memories are a bit off. (Kind of like how everyone who was around when Ruby shot Oswald SAY they saw it happen live, but actually only NBC caught it live -- CBS showed tape of it a few minutes later and ABC had to make do with film footage.)