The only connection between "Believe me etc" (is it one of Tommy Moore's tunes?) and Merle Travis' tune seems to be that both are in 3/4 and that both use notes from the gamut! :_)
I doubt by the way if there is any Irish connection as Ireland has no coal, and, as far as I know, no mines of any sort. This kept Ireland out of the major part of the Industrial Revolution and kept her poor, but on the other hand,it kept her clean!