Late in the book, 13th Stanza, section sixteen, in the dining room, Mia seems as surprised or more so than Susannah when see shes the skin behind the mask of the low man and low woman. Susannah feels genuinely sorry for Mia at this point. "Yes, Mia had lied and betrayed; yes, she had tried her best to get Eddie and Roland killed."

Around the same place in the story, the second time on the allure, it is Mia who calls Susannah to her dogan, the allure, Mia's dogan. And perhaps just as Susannah was able to communicate with Eddie in Susannah's dogan, Mia was able to communicate with others through her dogan.

As to the idea that probably generated the question, since the two pairs were sent to the places the other pair intended to go...I dunno, maybe it relates to the door that was used, some kind of baleful influence.