I agree with Jim Carroll that it's better to find out as much as you can about a song before you sing it, and not just copy the arrangement of somebody else you have heard, in his example the singer who copied Martin Carthy instead of listening to Harry Cox.

What you need to do is to get past the performer at the song itself, i.e. get the lyrics and tune in as pure a form as possible, and then apply your own interpretation to it. For all I know, in the above example, Harry Cox could have sung the song with his own 'mannerisms and peculiarities', and even if the singer in question had copied him rather than Martin Carthy, she would still not have been singing the song 'correctly'.

Assuming (in this particular example) Harry Cox provided the earliest known example of the song being sung in recorded form, how do we know he is 'right'? For all we know he could have changed the tune or the lyrics, perhaps unconsciously - I'm not suggesting he did, but the point is, he could have, without anyone knowing.