Offending the Analyst, the view "if you need to use statistics, then you have not designed your experiment very well".

[eppur_se_muova]

4. I can understand what they're saying -- if statistics are all you have, that might draw skepticism -- but some things

can ONLY be approached w/statistics, especially where medicine (human or otherwise) is involved.

Using metformin within 3 months of infection may reduce long COVID risk https://www.medicalnewstoday.com/articles/common-diabetes-drug-metformin-within-3-months-infection-may-reduce-long-covid-risk
(No, this didn't require the "forbidden experiment" -- human subjects as guinea pigs -- but rather an analysis of a 'natural' experiment which could be extracted from the medical records of a large body of subjects, and their conclusion(s) rested on statistics by necessity.)

Benefits of Wasabi Supplements with 6-MSITC (6-Methylsulfinyl Hexyl Isothiocyanate) on Memory Functioning in Healthy Adults Aged 60 Years and Older: Evidence from a Double-Blinded Randomized Controlled Trial
https://pmc.ncbi.nlm.nih.gov/articles/PMC10648564/#sec3-nutrients-15-04608
(Here, the investigators were looking for what might be a small effect using a relatively small number of subjects, who could not be screened for every factor of interest (the need to check for sexual differences was pointed out by the authors). Statistical analysis of similar studies made it possible to choose the size of the two groups of patients required to observe significant results, and it's hard to see how the results could have been found without extensive stats analysis.)

Of course, the view of many in the public audience is that there are "lies, damned lies, and then there are statistics", having seen battles of public opinion powered by demagogic manipulation of statistics, which most people don't understand at all well. People need to understand that it is the manipulators who have malevolent intent; the statistics themselves are neutral, even if not popular, and only a few know how to grasp the arguments involved -- many of whom are paid handsomely to use, misuse, and abuse them to benefit their clients -- hence, in part, the suspicions behind that expression in the paper. However, I note that the authors respond to that POV quite ably, in the text immediately following:

5.2. Why do we need statistical analysis?
We are familiar with the view “if you need to use statistics, then you have not designed your experiment very well”. This ignores the fundamental facts of life; we need statistics because we need to recognise and handle variation. Variation, arises because of the fundamental uncertainty in our measurements, in our sampling and from simply recognising that if we were able to repeat the sampling and monitoring we would get different results. And because we want to make inferences and predictions (i.e. not simply about the sample of animals we have observed but about the population of animals (most of whom we have not observed)).

If these were politicians instead of scientists, they would have introduced the discussion with "I'm glad you asked me that question", which is standard code for "I came prepared with a thorough rebuttal to this claim, and a rebuke to those who propagate it, so turn me loose!". IMHO they quashed the objection pretty thoroughly, so no need to prickle so.