The conflation of experimentally verifiable science and observational science (and, even more so, social sciences) is the crux of the issue. This is not to say that observational or social sciences are useless, but that they are less authoritative and more open to confounding variables than experimental science. People use the results of the later as if they have the authority of the former.
It is quite useful rhetorically and, unfortunately, as is so often the case, good rhetoric wins.
Whole fields have been devoted to defining science; I don't think experiment is necessary to the scientific endeavor. Experiments in many fields, for example, often suffer from problems related to generalizability or applicability to real-world scenarios. It's a major reason for observational science, although not the only one. Problems with replicability have also been shown to be just as endemic to fields dominated by experiments as those more influenced by observation, if not more so, across different scales of analysis from the molecular to the societal.
I think a better definition of what science is is broader, something like "logical argument based on empirical observations," although that too isn't right. I think the appeal of experiments is in line with that, to the extent that you accept that the experimental rationale involves a logical argument pertaining to randomization over potential confounds.
The underlying problem being discussed in the article, to me, is the denial by scientists that science is fundamentally a human endeavor, subject to all the problems of humans: things like greed, deceit, ideology, and so forth. Scientists like to pretend that they are somehow above all that, which means they pretend it doesn't exist, which makes the effects of human weaknesses in science all the more insidious. We see this play out with the problems in academics, financial conflicts of interest, and so forth.
What happens is that a certain cultural subgroup, already primed to be skeptical of science through their social context, recognizes the human weaknesses of science. They then make the mistake of rejecting science wholesale because of this. Scientists, in turn, often make the mistake of rejecting the notion of human influences on science, thereby placing undue confidence in their conclusions, leading to a lack of accountability or explanation when failures occur. Some degree of evolution in scientific theory is due to random variation, or lack of appropriate data, but some of it is due to human factors.
The conflation of experimentally verifiable science and observational science (and, even more so, social sciences) is the crux of the issue. This is not to say that observational or social sciences are useless, but that they are less authoritative and more open to confounding variables than experimental science. People use the results of the later as if they have the authority of the former.
It is quite useful rhetorically and, unfortunately, as is so often the case, good rhetoric wins.
What, do you hate science?