I think it's really deftly done here especially. It's still Babs who figures it out, so it's not a knock on her ability to solve the case. But she never could have gotten past her emotional investment to think clearly if not for Alfred's awesome incarnate nature, so he becomes essential to the resolution. It's a perfect balance.

Also, he sends her pie. Me, I'd have had her washing dishes or something that she'd never see a return on, and that is why I will never be as badass as Alfred.