I have never heard a singer falsely represent an English folk song as an Irish folk song in an introduction

You don't need to do that explicitly to spread the lie. People will assume that a song is Irish if they know it only from the Dubliners and the Pogues, or from compilations (like the one we started with) that are simply described as "Irish music" without qualification.

And if you're getting bored with having the lie pointed out to you, tough. Are we supposed to believe Obama was born in Kenya because millions of people said that for years? The more widespread and persistent misinformation gets, the greater your obligation to do something about it.