I only skimmed it so far but am having trouble believing it too. All their regression lines very clearly show a positive association between the variables, and it seems that they only failed to reject the null hypothesis because they didn't have a large enough sample size.

Also, regarding the bodybuilders, note that this study only measured the normal "day-to-day changes", and if we were to extrapolate their findings, it would likely show a much larger association when given exogenous testosterone.