From what I understand, ASCAP makes a blanket judgement regarding public domain and traditional material. For example, John Hardy is a tradional song in the public domain. BUT...ASCAP probably has at least a dozen copyrighted arrangements of it, so if it is performed, the assumption is that the version is close enough to a copyrighted version to require approval by ASCAP.
You want to contest it? ASCAP brags in their own literature that their fees and fines are legally unchallengeable. Most venue-owners will pay the 400 dollar (or more) extortion, rather than face possible fines up to 25,000 dollars.
And Mr Moe, if I play White Freightliner, I have few objections if a percentage of the fee goes to the estate of Townes van Zandt. But the fact is, it doesn't work that way. ASCAP monitors radio playlists at random, and money is paid to artists on the basis of the frequency with which an artist's work is played. So Lady Gaga is much more likely to get it. Secondly, ASCAP has one of the largest administration cost percentages of any supposed non-profit organization, with a big proportion of these fees going to salaries, office rental, and legal staff.