They should have had a control group that similarly did a small daily "fasting" kind of lifestyle limit that made them feel vaguely virtuous, and got tracked an reaffirmed. Like asked them to reduce their "sugar intake" or take the stairs more often or reduce "junk" food or drink water instead of a soft drink at their meal or whatever. Following something like that really tends to create a good feeling, that is totally independent from whatever the habit or changing it accomplishes. Just successfully doing the fast gives that accomplishment kick, which makes you feel better about yourself and thus presumably would show up in self reported depression levels.