Yogurt for fat was one of many lovely tips to come out of the oh-so-fattening low-fat 90s. I never tried it myself but remember seeing it in a Dannon ad.
I have actually never made brownies! Not that I won't eat them, I just don't like them enough to make them. If I were to make them and wanted to cut the fat - I would try to cut it, not eliminate it - I would try prune. I have read prune is a good fat fill in for heavy, dark baked goods. I have used part applesauce, part oil in banana bread with excellent results, I would think prune would be good in brownies.
I have seen the no-pudge brownie mix and had them once, at a friend's house... a very weird IMO low-fat Christmas dinner. Just wrong. BUT the brownies were good IIRC... so yogurt may work but I would try prune, myself.
I understand why fruit puree works, but I don't understand why yogurt works, just that it's supposed to.