Actually that is not true.
Catholics have the obligation under Canon law to follow proper form. A marriage without Canonical form is not a valid wedding. If they did not indeed receive a dispensation from the Bishop then in fact they are not married. Annulments are granted from time to time precisely for this reason.
A priest who does not have the faculties to perform a marriage from a local bishop is not able to witness the sacrament and the weeding is invalid. For example wedding that have occurred in SSPX chapels are invalid since they do not have the faculties. Canon 1108.