I have a team that should not be capable of regularly defeating bosses. It has one level 10 bracchus, a level 8 kit, a level 4 lupin, and a level 3 patissier pandosa. If I just refresh over the boss encounter I don't get any items (evidenced by the activities that say find items in icerun not advancing) but it will count towards the defeat icerun bosses activity. I did test watching a battle. They lost. It didn't count, yet every time if I just refresh over the boss encounter it gets counted.
Very convenient for me but I am pretty sure this is a bug XD.