If this saying can be traced back to the historical Jesus, which many biblical scholars question, it remains true that Jesus would have been speaking about a Jewish marriage, which was ritually celebrated in two parts (beginning with betrothal) by the respective families, and did not require the presence of an official witness. Such a union did require formal dissolution for the parties to remarry, but -- as you point out -- there was never any indication that the parties were cut off from the life and worship of the faith community.  Whether these words, if historical, can be applied to contemporary situations is doubtful.