I'm not saying you should use the more advanced methods yourself. I am saying it's a bit rich to criticise the results of the study without understanding the maths they used.
I'm not meaning to insult you with my messages. I'm getting frustrated with a fundamental difference between us. There are a very few things I'm an expert at. I have a passing knowledge of a few more areas (including stats). I often have to deal in fields I'm not familiar, or have access to more qualified people than myself. In those cases, I'll absolutely defer to those people. And I'd instantly defer to you in an area you are more skilled or experienced. It's not about "faith", it's the fact I have to prioritise what I'm going to learn for myself, and what I am going to have to rely on others for.
I strongly suspect you didn't know there was such a thing as statistical analysis until yesterday. But rather than acknowledging that it's an area you don't know about, you dug in and sought to "prove" that your preconceptions were right. What frustrates me, is that you've had a lot of information spoon fed to you in this thread. I'm no stats expert, but clearly have a better understanding of this stuff than you. Any time I've pointed you to information or the writings of actual experts, you've ignored it, demanded I provide you something different, sought out evidence to contradict the experts, and complained that I won't explain a really advanced technique to you (which would require many hours or even weeks on your part to learn just the underlying concepts they're based on).
Seriously, if you want to learn about this stuff, start with the CDC course you linked to. That will give you a really good start on the epidemiological concepts but not the statistical analysis side.
It's the statistical analysis that allows us to develop these incredible medicines so quickly. Statistical analysis not only gives us a strong understanding of the benefits and risks of these medicines, but also tell us how strong our understanding is so we can decide if we're going to test things more or not.
If you want to learn the analysis methods, you'll need something more in depth. Something like https://www.coursera.org/learn/stanford-statistics from Stanford will set you up really well. It claims to be free, but I seem to recall something funky with Coursera's definition of "free". Your other options are uni courses, a night school, or your state's vocational training system (Like TAFE in NSW), but they're going to set you back a lot more than any Coursera subscription.
That Stanford course won't go into the specific methods used in these kind of trials, but looking at the syllabus it should set you up enough to be able to do your own simple analyses, and digest a lot of other ideas even just by reading their Wikipedia articles. The Sampling Distribution and Regression topics are reasonably advanced - the kind of stuff you'd see in a 1st year uni course, and form the basis of analysing most real-world stats.