Even in science there is not a 'requirement' that you have a controlled experiment in order to have evidence that a claim is true. Following your argument you can't substantiate that humans are the result of evolution because we can't take two groups of early primates, subject one to evolutionary forces and the other not and see what happens. Instead we can observe a chain of correlations with plausible mechanisms that indicate causation and say it's evidentiary. For example, data that indicates unvaccinated people died at a higher rate and data that indicates people who chose not to vaccinate self-report that the reason they made that choice was based on particular information that they believed. That would be evidence that helps substantiate the theory the information led to deaths. It's not 'proof'. We can't 'prove' that exposure to the information actually led to the decision (because people sometimes misattribute their own decisions) and it would be impractical to imagine we can collect vaccine-decision rationales from a large number of folks pre-death (though someone might have) and you can't attribute a particular death to a particular decision (because vaccines aren't perfectly protective) so you have to do statistics over a large sample. But the causal chain is entirely plausible based on everything I know and there's no reason to believe data around those correlations can't exist. And science isn't about 'proof'. Science is about theories that best explain a set of observations and in particular have predictive power. You almost never run experiments (in the 8th grade science fair sense) in fields like astronomy or geology, but we have strong 'substantiated' theories in those fields nonetheless.
A causal chain being plausible does not justify or substantiate a claim of causation.
I absolutely would say that we can't prove humans are the result of evolution. The theory seems very likely and explains what we have observed, but that's why its a theory and not a fact - its the last hypothesis standing and generally accepted but not proven.
My argument here isn't with whether the causation seemed likely, though we can have that debate if you prefer and we'd have to go deep down the accuracy and reliability of data reporting during the pandemic.
My argument is that we can't make blanket statements that misinformation killed people. Not only is that not a proven (or provable) fact, it skips past what we define as misinformation and ignores what was known at the time in favor of what we know today. Even if the data you to point to shows correlation and possible causation today, we didn't have that information during the pandemic st the time that YouTube was pulling down content for questioning efficacy or safety.
