You should read
the Skepdic's entry on full moon and lunar effects, which debunks and explains that there is
no correlation between a full moon and emergency room admissions, psychiatric admissions, etc.. While very few, occasional studies do point to some correlation, the majority (most of them) do not.
I say the cat and dog story falls nicely into the "few, occasional" studies - I'd be really surprised if the data could even be replicated several times in a row.