I don't mean to sound condescending, but if science as a concept 'says' anything, it is exactly that truth must be verifiable.
There absolutely are problems with how study results are weighted. Starting from the way the press reports on findings, up to and including the uncritical acceptance of questionable material by many members of the scientific community.
However, there is no workable alternative to the process of science, because defaulting to whatever people personally like and discarding any inpportune data is certainly not how we move forward as a civilization if we have any ambition to continue our ascent (and we might in fact not have that ambition, but I do like to pretend that we do).
Studies and data in general must be weighted. Sometimes the proper weight is zero. I see little other options but to continue stumbling towards improvement and knowledge. Acting on data will always be an imperfect process on a sliding scale, very few people would disagree with that.
Edit: I would also say that there is a distinction between the opinion that we're generally moving too fast and the opinion that we have severe deficits in how we weigh incoming data. Both of these can be addressed, although the solutions appear to be way easier in the former case. We need to be honest about which camp we're in though.
In science as cumulative evidence, studies can in fact be harmful. If they are wrong or highly ambiguous, or if they make it hard to uncover errors, then they make it more difficult for future research to be correct.
The reasons include publication bias (rejecting studies with null effects and/or contradicting previous literature), p-hacking and so on.
That's why it is so important to apply rigorous standards everywhere: Transparency, data sharing, peer review, replication, pre-registration. In other words: There is no alternative to open science.
On the contrary, truth must be falsifiable [1]. The value of a theory is not in how easy it is to verify, but in how easily it could possibly be refuted.
[1] https://science.jrank.org/pages/9302/Falsifiability-Popper-s...
Just because science says something doesn't mean it's true. Truth must be verifiable. It's possible to easily and cheaply verify basic physical concepts like gravity. This inspires trust. Professors routinely reproduce physics in classrooms:
https://youtu.be/hezfZ91ayiA
Reproducing some medical experiment is hard, expensive and time consuming. Once a study is published, a huge number of people will simply assume it is true. Very few will actually check the methodology of the study. Virtually none will attempt to reproduce it.