Christ replied to the Scribes and Pharisees who were testing Him about the Law of Moses in particular. His teaching therefore applied to marriage under the Old Law.
The Church holds that all marriages between baptised non-Catholics as sacramentally valid, wherever they take place as long as the conditions for a valid marriage are present. So no, no spouse in a civil marriage is totally free to get a divorce and remarry. As far as the Church is concerned civil marriage between baptised non-Catholics is presumed valid and no different to a marriage between two Catholics in Church.
Natural marriages as far as I am aware cannot be dissolved if the unbaptised spouse does not wish to end the marriage. Perhaps you can refer me to any Canon law which states otherwise. 
Logic compels one to believe that the Law of God can never be out of synch with the teaching of the Church otherwise there is no way of discerning that which is bound in heaven and that which is bound upon earth.