Right, the parent post was making the same point: the article claims to have shown a lack of statistical correlation, but all they did was show that their study

Right, the parent post was making the same point: the article claims to have shown a lack of statistical correlation, but all they did was show that their study lacked the ability to detect correlation. It is a subtle movement of a few words, but they are important It can be interpreted in statistical terms. They could use the confidence interval instead to state that the study suggests infection reduces these adverse events by no more than half, nor increases their frequency by no more than triple.