Let me clarify.
When I speak of influence, I am not speaking about the influence tabloids have on people and their voting patterns. Instead, I am referring to "newspaper of record" type influence; news sources that will be used by academics and historians of the future to write the history of this era.
To expand on this a bit, the problem with right-wing media is that it is not taken seriously and a lot of it has to do with a lack of serious reporting. I find it very funny when right-wing media of one country refers to left-wing media of another country in their articles and programs because they are either unaware of local right-wing sources or simply do not trust them.