Well, 'Huntly by Carnie' is and always would have been incorrect, whatever your source is. Huntly and Cairnie/Cairney are two separate adjacent parishes in Aberdeenshire, therefore historically (quite apart from it being the bigger place) Huntly is not and never has been 'by Ca(i)rnie'. These days it's the other way round - an address in Cairnie is officially 'Cairnie, Huntly'.
The original document is available to view for a small fee at
www.scotlandspeople.gov.uk - see screenshot from the index to the Old Parish Registers - so you have the same access to it as anyone else, unless someone happened to be in a Scotland's People Centre, or if you or someone else can find a microfilm copy of the Cairnie/Cairney parish register.
As you can see, the date indexed is indeed 31 January 1766. However this could be the date when the banns were first proclaimed, or possibly the date when they were proclaimed for the third and final time, or possibly just the date when the parish clerk wrote it down. The original document may clarify this, but not necessarily.
It is unlikely to give you much more useful information, and in particular it will almost certainly not tell you the the names of the couple's parents.
