Maybe this is the other part of the story.

Are you saying they live apart but have regular social interactions?  Do they have access to each other's accommodation?  Do they have personal items stored in each other's home?

These may be pertinent facts that could influence the view of whether they actually live apart at all times during the year.  Think there are a couple rulings but you may like to start with Costa v. Commissioner, T.C. Memo.1990–572.