I was okay with everything you said until the last sentence. You seem to be double talking. If the reporting is false, doesn't that make it wrong? Or am I misinterpreting and there is a difference between false reporting and being wrong? And isn't false reporting by definition fake news? :shrug:
The reporting specific facts isn't wrong, but framing those facts to build a narrative that the facts don't really support is when it becomes hyperbolic or false reporting.