It's like acting, as someone has already pointed out, you become the character narrating the events of a song, telling the tale. In several of his songs, Steve Knightley of Show of Hands, talks about a fictional brother who always seems to be in some sort of trouble or other, it's all part of the make up of his songs, like a film, or a play.

In the case of political songs, I think that even if you don't agree with the sentiments of a political trad song, the very act of pulling it off for an audience, seeming to relate to the songs contents and sentiments, that's the victory and the mark of a good teller of the tale, good singer as it were.