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That's the same as in the UK, isn't it?

IIRC in the UK priests (in a wide sense of the word) can, and typically do, become Licensed Persons for the recording of marriages, whereupon no other officials are involved (except the ones the priests themselves send the paperwork off to). They do keep changing the rules on this, though: not so long ago, a marriage register was attached to a Licensed Place, not a Licensed Person.

Peter