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Perhaps they are right. Statistics in itself doesn't produce facts. It just transforms detailed data into aggregates. But if the detailed data is bad, the aggregates will be bad too.
There are fields where proper experiments are very hard, and usually the conclusions you can draw from the experiments they can do, are generally very limited. Then actually doing science properly will result in the field correctly being judged as being rather useless and funding being withdrawn. So the only way these fields can exist is by fraud and thus that it what they'll do.
For these fields, fraud is simply an evolutionary adaptation.
Can you provide examples of such fields? I am genuinely curious as one of my current interests is trying to figure out where we've actually hit hard or very large limits in scientific discovery. The problem is that simply "reading the current research" is literally impossible for someone who doesn't have a graduate understanding of math/physics/hard sciences.
Psychiatry is a good example. Since for the most part the diagnoses are based on symptoms, the experiments tend to check whether symptoms are reduced after treatment. However, it is very easy for the experimental setup to influence how people report things (since people's opinion of their symptoms tends to be fickle) and for the treatment to not allow for double-blinded experiments. For example, if you want to investigate whether transgender treatments have a positive effect on mental health, there is no such way to do things. And I know that there is a culture among at least a subset of transgender people of lying to medical professionals to get the care they want. The scientific field has a lack of focus on biased errors in their experiments, in contrast to random errors (for which p-values are often used).
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I am fine with admitting that there are worthy human endeavors where the scientific method and mathematical models are not the best way to tackle the question. If someone wants to study fairy tales or Greek mythology, I will not insist on them adding p-values to their publications.
But if a field pretends scientific rigor while just cargo culting, that will reliably enrage science geeks like me. I do not have a strong opinion on how much funding there should be available for studying the character of the wolf in Grimm's fairy tales. I do have a strong opinion on how much funding there should be for torturing statistics to 'scientifically prove' that the wolf is a negative character (p<0.05): the amount is zero.
I will grant you that the revealed preference of the funding agencies is different, though.
If I had my way, I would make big changes to the scientific reward structure (both funding and the 'impact' scores).
The end result should then be fewer original studies, but those should be done with more rigor (larger experiment sizes, having the preregistered experimental plans judged by an organization separate from the universities with very strong statistical expertise and specialized in finding those and other experimental weaknesses). And strong rewards for replication studies, with a base reward based on the impact of the original paper and then diminishing rewards if many replications are done, to encourage replications, in particular for very impactful studies.
Scientists could then still do investigative studies with less rigor, but those would also be rewarded less and be considered 2nd tier. To become a professor, one would then presumably have to have done at least one big boy study with the higher standards.
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