This is a more insidious problem than any one media property because the very structure of the local news organization -being small and distributed - gives them a unique credibility for most viewers because they assume that their local news team is more closely align with their local beliefs, values, and interests. People do not assume every word from a local news anchor is the exact script for the entire country.
Further, it is one thing for them to use the same script. It is entirely another thing for the script to be "you can't trust any other news outlet because they all report fake news with no research or verification. YOU CAN ONLY TRUST US". I have never seen that message on CNN. You may not like CNN's coverage of Trump, but they do not undermine every other media outlet.