Good question. I have wondered about that myself and it seems that the typical response is
- a mix of annoyance that a well-established fact is being questioned (a bit like how you would respond to someone who questioned if Kennedy was actually shot)
- a reference to some news story that was wrong; missing the obvious point single stories can't answer the wider question fo accuracy
- retreating to the alternative claim that the CNN is "biased" and at the very least as bad as outlet X.