Historically once people recognize the media is not trustworthy they discount it. You see this in the former USSR countries. People don't take the media seriously like they do in the west.
The most dangerous situation for a dictator is to be faced with multiple independent and competing sources of truth that all disagree with you, because they will propagandize your subjects away from you quite quickly.
They certainly do in Russia. People there (esp. older people) absolutely believe all the propaganda that's fed to them about the war in Ukraine by Russian state-owned media.