You don't need dishonest researchers to see this effect. You just need researchers who care, personally and/or professionally, about the impact of their work.
I'm sure Mr. Spock is a professor somewhere. If you talk to real working scientists, you'll find very few Spocks. Also, there are not a lot of Victorian gentleman-scientists; they all need to be funded...
Eh, the idea of "trust" gets into non-quantifiable territory very quickly. Further, your analogy with newspapers is, quite frankly, not good. I would say that generally speaking, if a newspaper consistently confirms one's biases it is more likely to be deemed "trustworthy" and vice-versa with "non-trustworthy" newspapers.
I'm sure Mr. Spock is a professor somewhere. If you talk to real working scientists, you'll find very few Spocks. Also, there are not a lot of Victorian gentleman-scientists; they all need to be funded...