It's not that your wrong. Giovanni has taken the responsibility of the squad I tried to establish that in his post skip posts. Yes he loves him some kido corp. But the kido corps is in the process of being fully integrated into squad five as a separate group within the squad. So at this point his focus is the unity of the squad as a whole and not necessarily only the kido corps. 

I did not mean for his introduction to come off as false. He leads squad five, I personally don't know any other way to establish that out side of paperwork and scheduling training exercises. And now updating records of the squad