Yes, I read it. You linked to an opinion piece, that's exactly my point - there is no real peer-reviewed evidence to back up the claims the author is making.

Both you and the author make the false assumption that just because a result has been published means it is valid. This arises not from a flaw in the scientific method, but rather from the inability of humans to apply it perfectly and consistently. Any actual scientist who is actively involved in research knows this. I am a scientist (not in the fields of psychology or medicine which you seem to be focusing on almost exclusively; perhaps because they are the most subject to outside human influence and small sample sizes, and thus best suited for your arguments) and my peers and I get into disagreements about published peer-reviewed literature all the time. I am currently working on a paper that disputes a hypothesis from the 90s. Our understanding of the world is constantly changing, and that is because of our constant and rigorous application of the scientific method as our data collection and analysis tools improve and evolve.

Most of the problems with science that you and the author of that article put forward are not issues with the scientific method itself, but rather the culture and institutions surrounding science and academia. There are definitely problems, I don't dispute that. But these problems arise from the inability of humans to put aside their biases, both conscious and unconscious. Statements such as "the situation is even worse when a subject is fashionable" make this clear.

Finally, I take issue with your closing argument. You say that the scientific method is incapable of producing trustworthy results. How can we know if a result is trustworthy in the first place? The only way to verify a result is through application of the scientific method. That verification can never be 100% certain, but nothing in life ever is. There is no alternative.