This article is about MD doctors, not scientists (although there may be some MD-PhDs in it, and yes MDs can get research positions).
MD doctors poll at extraordinarily high levels of trust, over almost any other professional group in the United States. So it really isn't correct to directly link this article's topic to "distrust". The effect you're talking about may exist in science, but this article is essentially a counter example to the effect you propose: clinicians publishing bullshit, but retain a high level of public trust.
Especially because the article is basically entirely quoting practicing scientists who identified this problem in the first place! More real scientific training or collaborating for clinicians who want to (or have to) do research could potentially improve the situation.
MD doctors (and even to a large extent DO doctors nowadays) are philosophically grounded on science. An MD fundamentally practices science. That used to be one of the key differences between MD and DO physicians, but science has been so successful at advancing the standard of care that DOs cannot ignore it anymore. That's just to say that MDs are expected to be fluent in science and it's not some arbitrary expectation of bureaucracy run amok.