I'm kind of agreeing with everyone here. Like Don says if you are doing something in another dialect/language then surely you want to try and get it as well done as you can? Totally agree with Tattie Bogle. Burns wrote some works in a broader Scots dialect; some works in a less broad more anglicised dialect; some works in standard English; and in some he chops and changes within the piece itself. Most famously in Tam O'Shanter. The bulk of the poem is in Scots then the middle section is standard English. Many Scots even speak like that changing from minute to minute. Why not in a song if someone wants to anglicise a line then try it. Sometimes it will work - sometimes it may not.

Scots themselves differ as to how they sing certain songs with some using a heavier dialect than others.

I agree with MG too that the songs are not only Scottish heritage. Basically I am not trying to proscribe people from doing them. I am happy if they do them. I am not sugesting that they should or shouldn't anglicise the words. In some cases it will work in others less so but there is no harm in trying. I just find nothing unusual about people using the Scots words without reverting to the adoption of an OTT Scottish accent, and tend to prefer it, because adopting an accent can often sound comical and like Jim says the bad accent overshadows the song. To me on balance it is better for (especially on a serious piece) the song to sound slightly different and unusual than it is for it to sound plain comical.