Wrong. Seems you forgot that Naruto made 12 clones before meeting up with Nagato and Itachi so they were fighting Naruto at 1/13th the power. To compare Itachi to BM is a big fail when he didn't have a notable edge over a weaken Naruto who was in intense training even before entering the war so he wasn't even at full power when he entered the war. Naruto telling Bee to watch out for Itachi's genjutsu did nothing, Naruto was not a perfect Jinchuuriki at that time nor was it shown Bee telling him perfect Jinchuuriki can easily breakout of genjutsus as Bee actually did to Itachi genjutsu.
Bee had no knowledge on Nagato and was caught while trying to help Naruto who is not at full power, was in intense training and is not a perfect Jinchuuriki. BM is a huge gap from KM, KM is some of Kurama's chakra while BM is access to all of it; he deflected 5 tbbs. Also Naruto was still talking to them at the start of the fight because Kabuto left their personality still intact until he took control of Nagato. SM Naruto (war arc SM who is able to fuse with toad sages) is capable of beating Itachi so don't even compare him to KM let alone BM when Naruto is at full power and not 1/13th the power after intense training.