It is no secret that the media can put their own spin on the news. Anyone who says anything only sees it from their perspective. Unless just stating the facts, these statements are merely opinions. If something "unflattering" was stated about the president-elect, then he and his supporters should have the right to respond.
The media has lost almost all credibility during this election process. Not one major news outlet had a poll that showed Trump winning, and we all know what happened on election night. The media needs to be more worried about winning trust back and being honest than Trump's possible name-calling.
The President should be able to express an opinion like everyone else. When people say things that he thinks are untrue that are about him, he should be able to say that these things are untrue. His reelection changes depend on it, as well as his abilities to get things passed in Congress.
Yes, the president should be able to accuse the media of falsifying some stories if the outlets do not have substantial proof that the story is true. If substantial evidence is presented that the story is true, no one will believe Trump's claim that the story was false. The media bears the responsibility of validating its stories.
The question is regarding a President or President elect, not an ordinary citizen. Once you assume that public office you now speak on behalf of your constituents, not your personal beliefs. This is seen within the military as well. A citizen can criticize the Joint chiefs of staff publicly. However, a military member cannot.
An individual who holds a public office holds great power in their words. And by stating something without evidence is putting the defender in a state of guilty until proven innocent.