Not sure if they have the brain function that allows higher functions like love, empathy and depression. Depression, in humans at least, is caused by a low level of serotonin. Depression occurs in a very specific area of the brain (maybe brain stem or frontal lobes) and is there any proof that bettas have that??
**it might be totally different in a fish their size.
But to be safe, I would attribute the "depression" to stress or familiarity moreso than a complex brain function like depression.
Also, +1 to the slime coat thing. Lude shed his slime once!! It's not nice and people who pet their fish can activate that. Maybe the fish was "special" ;p