"Hunters of Kentucky" first campaign song?

I’ve read that “Hunters of Kentucky”, used by Andrew Jackson, is considered the first campaign song.

But Oscar Brand recorded a collection of campaign songs going back to…well, Washington. They really do seem to promote the historical presidential candidates and I read somewhere that “Jefferson and Liberty,” for example, was popular during the election.

So what makes “Hunters of Kentucky” considered the first campaign song?

(For bonus points: If somebody knows of any campaign songs the Wikipedia list and Oscar Brand’s album are missing, I’d be much obliged. I just noticed that Brand’s doesn’t include McGovern’s and the Wikipedia list doesn’t include Van Buren’s, so maybe there are some songs missing from both lists which I haven’t caught yet)