I did a quick skim and the main problems with the study are:
1. no placebo, so it's unclear whether it was actually due to the flu virus or some unrelated factor. The study admits this might be an issue, but casually dismisses it with "We looked for this, and found no such effects."
2. the "flu virus" in question is actually a vaccine. Needless to say there's a big difference between getting a flu shot and an actual flu.
Am I an idiot or is this clearly non-causal?