> although it must be over two hundred years in these parts, is still sung to the air of The Uist Tramping Song,

Given the 1937 copyright information, the simplest interpretation of the above is that the writer believed

a) that "False Knight" had been sung in those parts for over 200 years, and

b) that the "Uist Tramping Song" (or its tune) is over 200 years old, and

c) that the ballad is currently sung to the tune of the "Tramping Song."

Without two-centuries-old evidence to back it up, there's no reason to assume that *either* belief "a" or "b" is necessarily true.

"C," however, is evidently factual.

If "a" and "b" are supportable, there will be contemporaneous evidence. We can't logically assume it is exists unless we see it.