I don't think so. Sometimes composers might unwittingly appropriate tunes from other sources. But since Lerner and Lowe have produced so many memorable tunes such as found in My Fair Lady and other musical scores, it seems unlikely that Lowe would base it on anything ethnic unless he intended to use it for a characterization. Now in Brigadoon, there may be some basis for Scottish tunes.

Tommy was pulling the proverbial leg I think.