Okay, but who are these people, where's their data coming from and are they reliable sources? Is this not just some sort of quasi-open forum where pretty much any old chump off the street can sling together some slides and have their five minutes of waffle?
1)
The fuckwit at 4:20:10 is just a crank anti-vaxxer of no relevant expertise who is touting fraudulent science and bullshit.
2)
The guy before (the Louisiana doctor) starts off making a reasonable point... and towards the end it gets messy. He's right that an initial trial is unlikely to have sufficient power to determine incidence of very rare adverse side effects. A trial of 100,000 people is a really big trial with a lot of people. But it's unlikely to pick up a 1/100,000 rare adverse effect: you'd need millions of subjects to spot it. For a specific age group, which might be just 10,000 people of the 100,000, whilst that's still a lot of people, it will have even less ability to spot such rare effects.
But this is a known issue. Drugs and vaccines are approved after phase 3 clinical trials. In fact, there's a fourth phase to clinical trials - post-approval safety and efficacy studies to pick up this sort of thing. And it's here he goes a bit wrong. Firstly, he criticises the observational trials as inadequate - yet he is using information from these post-approval observational studies (re. myocarditis risk) to argue his point. He can't claim studies are inadequate and then treat them as a cornerstone of his own case. Next, he's just unaware of practicalities. I appreciate what he wants and the rationale for it, but running phase 3 clinical trials of the size required to find out what he wants would be staggeringly expensive and time-consuming beyond reasonable attainment.