Art gave the shed without mentioning it to Karen. if Karen's account of her & Art's relationship is accurate, that's a BIG red flag. just sayin'.
I think that was more of a manchild doing a naughty thing behind mama's back, knowing she wouldn't approve. As they get older, a lot of men seem to want their wives to be their mothers for some reason, probably so they can periodically assert their independence by acting out. Since Airyn was too young, he recruited Karen. Who knows how far he took it.
Eberhardt's comment sure makes me think, but without context he could just be referring to the male/female host issue he's known for raising, not doing the nasty.
