I don't have the Curious Collection of Scots Tunes (Edinburgh 1740) or even the Collection of Curious Scots Tunes (London 1743), but I do have Charlie Gore's Scottish Fiddle Music Index, which tells me "Barbara Allan" is in both, with the same theme code as the CPC version.

Gore's theme code also matches "The Old Woman in the Glen", in Charles Maclean's Collection of Favourite Scots Tunes posted posthumously in 1774. Maclean was a major contributor to the Macfarlan Manuscript of 1740, left for London shortly afterwards and seems to have had nothing to do with Scottish music once he got there, so his version may be contemporaneous with Oswald's earliest and he may have been Oswald's source. (David Johnson wrote an entry on Maclean for the Grove - he didn't have much to go on and I can't remember where I put his preprint, I don't have access to Grove here). Maclean's title sounds to me like it might have been of Gaelic origin, in which case Oswald might have been making up the link with the older Barbara Allan song. Oswald made a lot of stuff up.