That's not true, if a piece of economic information would be damaging to Trump it would likely get even more coverage.
He's also gamed them a few times to accidentally cover good data. Most notably when he "leaked" the low jobs numbers and CNN/NYT covered it non stop
Isn’t that the opposite of influence though?
Not if you know how to spin it. Like him or not, Trump is unquestionably good at getting 'bad' press to work in his favor. Any power, positive or negative, can be harnessed if you are clever enough. To what end, well, thats a different discussion.
In certain media but in other media the opposite it true. The top cable news network for the last decade has been conservative (Fox obviously) and conservative media absolutely dominates talk radio and it also has a robust Internet presence.