So I am not sure if anyone has discussed about his recording ability but i think its simple. Since now we know that Black Zetsu is Madaras will it is safe to say that he uses genjutsu to record the abilities. Both Hashirama and Madara were both capable of genjutsu so it is very likely that he just uses his own genjutsu on Obito to learn about Itachi and Sasukes fight. I know there isnt any pictures or anything but i dont see this as a huge thing.