It should perhaps be pointed out that the copyright in an arrangement and the copyright in the song itself are quite separate things. The arranger cannot claim copyright over the song itself. Where royalties are payable, these are shared between the arranger and the composer. Where the composer is "trad" that doesn't increase the arranger's share. Furthermore there has to be a degree of complexity and originality for the arrangement to be copyright, simply putting the three chord trick to a melody isn't sufficient.

The same goes for transcribing a traditional song - the transcription is copyright, not the song itself. No one can reproduce that particular transcription without permission, but they can make their own transcription from the original source and they will own the copyright in that.

This gives musicians protection for their own artistic contribution while leaving the original material in the public domain.

There may have been cases where others have succeeded in registering copyright in a traditional song to which they are not entitled. The copyright agencies cannot be expected to know the entire corpus of music they manage, so mistakes can be made. Where there is a known composer they can be expected to protect their own copyright, but folk songs don't have the same protection unless someone is willing to challenge an unjustified claim. Kennedy got away with his alleged activities because no one was able to challenge him. That is a fault in the system but it is one of enforcement, not principle.