I wonder if Akane and the house being summoned is actually NOT a mistake.
i.e. Akane herself is in a sense a priestess, but unlike the Hiyori who purifies miasma, Akane is more of blessing type, like feeding the land god here.
And the house is essentially her sanctuary/temple...
Well, if the pig shows up again occasionally to have her cook for him, or if it tell other gods about her and they show up, then I'm going to go with that explanation in my head.