One can find contradictory claims out there. Here is an English version of the marriage law. There is a surprising amount of legal rigamarole (in Norway, as well) pertaining to clearing "impediments". Assuming that the parties have done their part, then we move to Chapter 4. Article 16:
Marriage may take place before a minister of the church, a
representative of a registered religious organization empowered to
perform such ceremonies, cf. Article 17, or before a civil official so
So turning to Article 17:
Religious solemnization of marriage shall be performed by the
ministers of the National Church, and priests or other representatives
of registered religious organizations in Iceland who have been
empowered to perform such ceremonies by the Ministry of Justice and
and that is now part of the Ministry of the Interior. I can't find any indication that ULC has been approved. There are 49 religions officially listed by Statistics Iceland, including Siðmennt, a secular humanist organization which gained official status on May 3rd, 2013 when
the organization was officially registered as a secular life stance
organization under a law passed in the Icelandic Parliament on January
30th of that year. A formal ceremony was held by the Interior Minister
Ögmundur Jónasson who had strongly supported our cause, to mark this
historical event. As a result, Siðmennt gained the same legal and
funding status as religious life stance organizations in Iceland.
Weddings conducted by Siðmennt celebrants since then are legal and
couples no longer have to go to government offices for that purpose.
In light of the fact that Siðmennt is officially listed and ULC is not listed, I would conclude that you did not accidentally marry anyone, even if they had dealt with the impediments.