That was my original thought, however if you want to quantify an effect it would be ideal to measure the same trait in both parent and offspring. I assume that the reason that this was done (I didn’t read the papers) is because this is a retrospective study, where the participants self-report on the exercise level of their fathers, rather than a longitudinal study which could measure the fathers’ metabolic state fitness at time of conception.

Thus, although there is a plausible link, I now agree with the parent post that this is sufficient reason to take the study with a grain of salt (given well known academic incentives to produce positive results, etc).