Why did Mido rule out Masahiko Kida as the Yotsuba Kira purely based on him providing the account for funds used to commision Eraldo Coil?

Question

I rewatched the yotsuba arc and never really understood the logic.

Kira would want L's name and face, so why would Masahiko Kida be proven to not be Kira if he set up the account of funds for Eraldo Coil with the purpose of finding out L's identity?