I was alive and watching the news back then, and this is bullshit. NYT didn't admit their screw-up until over a year after the war began. [0] I'm not sure CNN ever admitted it. Even worse, every time the previous ridiculous theory of war was exposed as nonsense, they were eager to transfer to the next ridiculous theory: WMDs, Saddam supposedly harboring aQ, fostering democracy, saving the Shiites, saving the women, saving the Kurds, saving the Yazidis, the surge, opposing MaS, opposing ISIS, opposing Iran, opposing corruption, stealing their oil, etc, blah, blah, blah.
I was alive and watching the news, and you're completely wrong about TV news and the NY Times reporting, which freely admitted that Iraq didn't have a chemical weapons program (except for Fox News, which kept reporting that this time we found it without ever reporting that the last time wasn't what they suggested). The only thing that took a while was the apology for believing Bush administration sources in the run-up to the war.
The simple way to show that anyone on TV (besides e.g. "Democracy Now") got it right by a particular date would be to link to a recording or transcript of an example.
Here's the NY Times less than a month into the invasion noting that no active chemical weapons program had been found and that the administration's words seemed to be shifting about whether they believed it would ever be found: https://www.nytimes.com/2003/04/05/world/a-nation-at-war-ill...
[0] https://www.nytimes.com/2004/05/26/world/from-the-editors-th...