Okay, before you give a huge duh, let's consider this for a moment. According to the abstract:
Both TV news and newspaper use contribute to an increase in political and nonpolitical engagement, but fail to affect trust building in politics and among people in general.Unfortunately I can't call up the entire article, at least not easily, but they rely on American National Elections Study data, a source I often use as well, so I'm assuming the quote above includes the traditional newspaper and television news exposure items. It's hardly surprising that media consumption is associated with, or contributes to, increases in both political and non-political engagement.
But you may be surprised that these media exposure items are unrelated to trust. It's not surprising. Greater media use tends to be found among those with greater motivation to keep up with, or be involved in, public affairs. These folks are often quoted, or know others who are quoted, by the news. Or they're deeply involved in topics that the news media cover, so they see all the nuances and therefore see how the news, especially TV news, often tosses out nuance in order to explain what's happening to a general audience. The result? Less trust, or enough so that an expected positive association becomes no association between consumption of the news and trust.