Trump appears to be basing his 'legal' argument on one of those nutjob James O'Keefe's undercover videos, which most people say was a total disaster, but Trump latched onto it because it was directed at CNN and, at least from his point view, confirmed his warped view of CNN and the media in general.
Trump Writes Unhinged ‘Legal’ Letter Demanding That CNN Pay Him Money
http://nymag.com/intelligencer/2019/10/trump-letter-cnn-project-veritas-first-amendment.html