They do perform a statistical analysis ("propensity score matching") to try to control for off-target correlations, but its true that the entire strength of the paper revolves around this having been done correctly and it being sufficient. Given the fact that improperly controlling for confounding factors could entirely account for their data (people whose personality traits are deteriorating are likely to have some awareness of this, and therefore to seek therapy) you would think that an account of this procedure would be front-in-center of their argument- but no, all details of that step are relegated to supplemental data for some reason.

It's also worth noting that data collection was entirely done through surveys; so, another explanation could be that therapy simply made people more aware of pre-existing personality deficits, that they were then able to more accurately report.

And further, even if the results are valid, it doesn't invalidate the benefits of therapy; most therapy methods are built around helping the patient. Its possible that therapy improves the subjective quality of the patient's life at the expense of some external qualities (or pretense thereof.)