I've always assumed networks have a certain threshold for special coverage depending on the situation, and time of day. I distinctly remember the news of John McCain's death coming down during a Saturday College Football game. I'm unsure about other networks, but CBS ran what might have been a pre-taped Special Report during a 1st half commercial to announce his death, and then a long-form Special Report during halftime where they went into his life, legacy, etc.
Otherwise, I think networks do everything they can to avoid blowing out any portion of Primetime programming. During Trump's Impeachment Trial, CBS, ABC, NBC, and Fox all aired short and sweet wrap-up Special Reports at the very bottom of the hour before local programming on the East Coast. The only time I recall primetime programming getting trampled on is when Obama made his late evening announcement on the death of Bin-Laden, and the debacle that was network coverage after the Boston Marathon Bombings. I'll never forget every major network taking air to announce arrests had been made, only to find out minutes later that the rumor was untrue.
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Also, a small bit of history: I'm a huge NASCAR fan, and one of my first racing memories is a post-9/11 race at Charlotte Motor Speedway. NASCAR was minutes away from starting a race when Operation Enduring Freedom started/was announced. In the immediate chaos, the race was put in a hold, NBC's track team tossed to the network, and it took about 30 minutes for the race to get back on air on TNT and pre-race ceremonies to begin. NBC came back to the race with about 20 laps to go, marking the first (and only time that I know of) a race had been simulcast on two separate networks at the same time.
I'd be curious to know if any other sports had the same issue. I assume NFL Sunday's was as big in 2001 as it is now, so how did CBS, FOX, etc handle it all?