When setting up relationships in database view a individual relationship to an organization can be marked as "Contact" - and no contact type assigned. When this is done from web view on the relationship (when you select edit relationship) - there is a checkbox right above "Primary employement for <name>" that's called "<Name> is a Contact for <Org Name>".

If you try setting up the same relationship in web view that checkbox does not exist or appear. And you must choose a contact type to make the relationship a contact of the organization. But even removing contact type later on, doesn't cause the "Is Contact" box to appear.

So this seems limited to relationships that are only created in database view. We would like this fixed as we don't want a contact type to be used on many relationships.