Joe, it is evident that many (most) of the Carter songs predate the Carters. The problem is that slight word or tune changes make copyright possible. Then you have to show that your musicians are not deriving their versions from Carter Family versions.
This means that the court, publisher (Oasis in your case), etc. have to decide. If not schooled in the intricacies of copyright, and the history of these songs, they have to have everything laid out for them, or they probably will err on the side of caution.

In the post above, Richie says the Carters got "Cannonball" from Riddle. There is a small discussion posted above that. Is it Riddle's version? (Cohen disputed the connection; Riddle said he first met the Carters in 1934, but the Carter version dates from 1930. Riddle also said later he couldn't remember the tune, but also said he got the tune from his uncle. Rather confused). One may go through folksong collections and find similar words, and the tune, prior to the Carter copyright. But is the rewrite by the Carters (and/or Riddle) sufficient to fend off other versions? Are there other versions that leave out reference to McKinley? To paraphrase, it takes a heap o' lookin'.

Added note- I forgot to mention that Poole recorded "Whitehouse Blues" in 1926.