And sometimes they claim they wrote it! Like Wild Mountain Thyme, see also Braes of Balquidder.

Best to find a version which you can trace to a traditional or public domain source, i.e. a published collection. There is also at least one web site which lists songs which are Public DOmain in the USA - but be careful, UK and Europe are different. A song can be still in copyright in UK, but not in US.

Of the songs you listed, I know Bob Dylan did Man of Constant Sorrow, but I think the original may have been Girl of Constant Sorrow.