He would have a problem because it wasn't. McPeake is credited with the copyright of Wild Mountain Thyme because although the lyrics are closely related to Tannahill's the melody is entirely different and NOT The Three Carles o' Buchannan as suggested above. Tannahill wrote his song to The Three Carles but it was set, and printed, (after his death) to a version of an old tune, The Braes of Balquhidder, by his friend R A Smith who also printed the Three Carles tune in a volume of his Scotish (sic) Minstrelsy. Hamish Henderson made a mistake when writing the sleeve notes for a Scottish folk singer and names the tune as the Three Carles when in fact it was the McPeake's tune. The Braes tune, as has already been mentioned, was used by Burns among others.
I 'did' a Masters at Edinburgh Uni, tracing The Three Carles and The Braes melodies and Tannahill's poem/song, a fascinating journey.