Aside from the issue of the "Compulsory License", songs can be altered if
they are shown to be derived from earlier sources. In the case of a Dylan
song, or Woody Guthrie for example, many of the tunes derive from
antecedent ones. Even some of the subject matter for some of the songs
in the text that exist prior to the song in question can be altered.

Scarborough Fair, for example. The Canticle of Simon's is copyrightable
and can't be altered, but the song for the most part is in public domain as
a folk song. You could write another "Scarborough Fair" and not lose in court.

Folk music by definition requires that the songs change, mutate, or are
rewritten to accommodate later times historically. These become "variants"
of a possibly original text that has become anonymous or in public domain.

Frank