It's worth noting that whether in a religious marriage or a civil one, the the couple do not "get married" by the priest, minister or registrar (or whatever). The job of the priest etc etc is not to marry the couple, but to to act as a kind of special witness to a marrtiage actually carried out by the couple. In circumstances where it is impossible for the priest etc etc to be available, it's perfectly possible for the couple to marry in their absence.