In fact the Auld Lang Syne tune itself is a kind of "world music" adaptation. The reason Thomson picked it (perhaps at Burns's suggestion) was that it was a current popular hit, thanks to its use in William Shield's ballad opera "Rosina" - it features in a scene of peasant life, played on two bassoons in imitation of a bagpipe (not necessarily a Scottish pipe, as far as I know). The tune hadn't achieved any great popularity before that. Shield was from Newcastle and was interested in music from all over the place - he even went on a song collecting trip round Europe, despite having practically no money. So when he picked up the "Miller's Wedding" tune he was using something from another culture (albeit one not far away).

Thomson and Burns knew where Shield got it and what it had been used for in Scotland before, but their main motivation must have been that here was a terrific tune to be had for the asking, with no widely known song already using it, and with all the promo work already done thanks to Shield. It came via an English source, but so what - Burns had set words to English tunes before.