I also vaguely remember coming across a study showing that the previously well-established correlation between pet ownership and overall happiness was largely due to 2 factors:
not controlling for preexisting happiness/quality of life, since you are more likely to be happy in the future if you have been happy for a while already, and people are more likely to buy pets when they are financially stable (which is correlated with overall happiness)
small data sets not capturing a significant portion of the pet-owning population whose quality of life decreased after getting a pet