No, the source of CNN is always the same (the website stream). It doesn't matter who your provider is (Cable company, OTT company, CNN directly). How Channels works is that it logs into the website with your credentials, finds the stream, and redirects it. Either the stream that is being offered right now is not compatible with Channels or Channels needs to be updated to handle what is being offered.
Otherwise, you have to either grab the webpage on its is face (PrismCast) or/and grab the output of a streaming dongle (HDMI Encoder through ADBTuner, Roku Bridge, perhaps a few other options that have recently come out). Nothing more can be done.