First, Kimmel lied about the political affiliation of Charlie Kirk's assassin for political purposes:
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You can say "Oh, but he was mistaken!".
Then he should have issued a correction and apologized.
Instead, he has doubled down.
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Second, Fox News is a CABLE outlet, not subject to FCC rules for public broadcast license.
ABC as a broadcast license holder is under FCC jurisdiction and all the rules and regulations that entails.
Just the same way your Drivers License requires you to obey traffic rules and regulations or be subject to suspension.
And one of those rules is to not mislead the public intentionally.