The specific question in this thread relates to the surnames of children whose parents did not claim to be married when the birth was registered, so the question of how and when they were married does not arise, and any comments relating to the legality of the parents' marriage are irrelevant.
That specific question was also covered in the link I gave, I had tried to add the exact paragraph by time given but for some reason I could not make any changes to the post or indeed access any Rootschat lists until I had rebooted my computer, for which I apologise.
However if you open the link and scroll to Sir Patrick Fords extract timed as 12.30 p.m. you will see no witnesses to a statement of being married was required. Scottish law was very relaxed in that matter.
See
http://www.rootschat.com/links/01rtn/ Sir Patrick Ford 12.30 p.m. 4th paragraph
I remember a professor of Scottish law pointing out that there was actually a case with regard to inheritance which some Members seem to think does not matter, but it is, after all, an important point. There was an elderly spinster who lived in one parish and a minister of the Established Church or of the Free Church of Scotland who lived in another. They met at a tea party, and there they certainly did not get married, but they were attracted by each other. They never met again, but from their separate parishes they conducted a correspondence, and that correspondence developed so that it was obvious that they regarded themselves as man and wife. When he died, she put forward her claim as widow under the Scottish law, and, although there was nothing definite in that correspondence to show at what precise date they first recognised themselves as man and wife, it was decided, taking the whole gist of that correspondence over that period of years, that long before the death of the minister this lady was his wife, and she made good her claim to her part of his estate. I give that as an illustration of the peculiar difficulties which we have with regard to proof as to whether there was a state of matrimony or not.
In the above example there was no witness to a statement that they were man and wife but the gist of the correspondence between them lead to a court finding they were man and wife and allowed her claim to part of his estate. Thereby adding another example to the tombs of case law that may be used to aid a court to coming to a decision.
Cheers
Guy