I don’t disagree with your arithmetic, I am only pointing out problems with the interpretation. As @Sander has pointed out numerous times, frequentist model probabilities do not capture all uncertainties, and this presentation can be misleading in that it discourages not only thinking about the sampling model, but the possibility of being fed intentionally misleading information.
Critical thinking needs to be enhanced with quantitative skills. To evaluate evidence already collected is an inherently Bayesian activity:
https://academic.oup.com/jrsssa/article/168/2/267/7084313?login=false
This commentary on an Efron paper from 2010, he states the following:
First, I disagree that frequentism has supplied a good set of working rules. Instead, I argue that frequentism has been a prime source of reckless overconfidence in many fields (especially but not only in the form of 0.05-level testing; … The most aggressive modeling is that which fixes unknown parameters at some known constant like zero (whence they disappear from the model and are forgotten), thus generating overconfident inferences and an illusion of simplicity; such practice is a hallmark of conventional frequentist applications in observational studies.
These probabilities (False Discovery Rates) often require the use of Bayes theorem in order to be computed, and that presents special problems. Once data are observed, it is the false discovery rates that are the relevant assessments of uncertainty. The original frequency properties of the study design - the error rates - are no longer relevant. Failure to distinguish between these evidential metric leads to circular reasoning and irresolvable confusion about the interpretation of results as statistical evidence.
A proposal deserving serious consideration that reconciles frequentist estimates with Bayesian scientific concerns is the Reverse Bayes methodology, originally proposed by IJ Good and resurrected by Robert Matthews and Leonhardt Held.
Matthews Robert A. J. (2018) Beyond ‘significance’: principles and practice of the Analysis of Credibility R. Soc. open sci. 5: 171047. 171047 link
Held L, Matthews R, Ott M, Pawel S. Reverse-Bayes methods for evidence assessment and research synthesis. Res Syn Meth. 2022; 13(3): 295-314. link
For an application, see this post: