My example wasn't set up to avoid one class of data. I said that I might get wet for other, non-rain-related reasons. So there is data with me being wet and wit

My example wasn't set up to avoid one class of data. I said that I might get wet for other, non-rain-related reasons. So there is data with me being wet and with me being dry. And in the data, the observed correlation is zero, even though there is causation. That is because there is a confound. Also, in my toy example, the data collection process is not biased. You can collect the entire population of my days out, and you will still find no correlation. The problem is not sampling bias, it is an unobserved confound. That was just a toy example. But the linked paper may be an important real world example! You're right that "mask-wearing is only brought in when Covid is bad" is testable. Does the paper test it? Does it attempt to control for endogeneity of mask-wearing? If not, then it may be reporting a spurious null result. You're right that causation implies correlation in the following sense. "X causes Y" means that if we hold everything else equal, and change X, then Y changes. But that requires holding everything else equal. It's entirely possible that in the data we observe, we see no correlation, because an unobserved confound is biasing our estimates towards 0. That is why serious social scientists spend so much time looking for random variation, and worrying about unobserved confounds. In particular, it is just false to say "they found no correlation, so that proves no causation".