Thanks for the correction, that's the problem with stomping around in a bad mood

. I've modified my post accordingly, but my conclusion that these findings are unlikely to replicate or be biologically relevant ramains.
I agree with your criticisms. However, I do not find it unlikely that there could be associations between personality and immunity. Genes code for immunity, and genes code for personality. So it seems logical that there must exist certain genotypes, both with regard to immunity and personality. In other words, genes that code for say, high baseline inflammation, would also influence personality formation. Patterns of immunological "configuration" as well as patterns of personality.
Personality is just a higher level of phenotypical expression than the immune system. Anatomy (structure), biochemistry, personality, behavior - these are all phenotypical expressions of the same system, but described at different levels. The system is a whole. Personality cannot be separated from physiology. Of course, I'm just talking theory now.
Each additional test increases the chance of a false positive
Ok, I understand. This I believe is also known as "going fishing" in the data. If you pair enough variables, you will inevitably find correlations.