As Calisto is listening to Edgeworth's story about the knife, all she has to do is deny everything. Instead, she tries to come up with an explanation for how she could know the knife transforms; instead, just say that she never knew. If Edgeworth accuses her of being the Yatagarasu, there's no proof for that either, other than "It's the only way my theory about you knowing the knife trick could work." Also, one of the main points about the knife knowledge being secret is that Detective Badd didn't know about it. However, just speaking in generally,
incompetence is not impossible in the AA world.
Officer: Hey, chief! Chief! Take a look at this!
Badd: .....Mhm....
Officer: Look, see! This key...it can transform into a knife!
Badd: Yup, that's great, officer.
Officer: D-...Detective Badd, you're not even looking.
Badd: I'm sure it'll be vital evidence.