Ela pede peixe was demonstrated earlier in the lesson as, "she orders fish." Why is it okay to translate, "she orders," as, "ela pede," but not for this?
Because "she asks for fish" and "she orders fish" both are fine in English, but not when "She asks for the bill." You'd not order it, because ordering something, as Danmoller said, has the connotation of buying it. Think of the verb pedir as "to ask for/to request," to avoid confusion later.