First of all, Rabbi Brody has never said that psychiatric medications should never be used. In extreme cases and as a last resort, it’s likely he’d approve of it.
Second, it’s important to understand that there is a lot of controversy within the medical community on the effectiveness of anti-depressants. A recent meta-analysis claimed to show that most anti-depressants don’t really work at all (I think this was in Time or Newsweek). There is a significant amount of corruption within the pharmeceutical industry — they do something like commission 10 studies on the effectiveness of their drugs, and hide the results of the 8 studies that show no effect. Several books and films have appeared on this topic. In addition, many of these pills have serious side effects, including even such things as an increased risk of suicide attempts.
Third, there is a large amount of research showing that certain behaviors or dietary changes — exercise, praying, volunteering, being thankful, writing in a journal, dark chocolate, even cold showers — can improve mood and decrease depression just as well as, or even better than, anti-depressants.
Fourth, Rabbi Brody has counseled many people whose children were on medications like adderal or whatever, and through parenting and lifestyle changes helped them stop using the drugs. So some of what he’s saying comes from his counseling experience (as opposed to just his beliefs or whatever).
For these reasons, in all but the most extreme cases (for example, with lots of suicide ideation), I think it makes sense to pursue other avenues — such as hisbodedus, increasing one’s emuna, getting more sleep and exercise, eating healthier food including dark chocolate, increasing social contact, etc. — before resorting to medications.