Not trying to be controversial, but the problem with studies like this is that it is almost impossible to factor in all variables, and too easy to jump to conclusions that may or may not be correct.
Something we all know is that pets tend to be a part of more established, traditional family structures. Pets are an expense, so homes with pets tend to have parents that hold steady jobs. So well-adjusted kids growing up with pets might (and probably) is more a result of those kids growing up in more stable family structures, and pets just happen to be a part of that home structure. Pets being in those homes is probably the result of the homes being more stable, not the cause.
Statistics are nice, but interpretation of those statistics is extremely difficult.