Then their "case" (legal or business one), however bad it is now, is in even deeper doo-doo:
1. Headlines for the same [and edited from the same "base"] articles may be different depending on publication.
2. News headlines, just like titles of the books and movies cannot be copyrighted, they are exempt.
Note that however valid your points are for copyright issues, this is not necessarily a direct copyright-violation issue (though, again, IANAL). Misappropriation doctrine is a separate issue, and so the headline-copyright exemption doesn't apply. Though the NBA v. Motorola case weakened the issue somewhat, I don't think the factors mentioned in that case are applicable to provide cover for AP headline misappropriation claims.
As to your first point, the basic premise of INS v. AP seems to have been held through the more recent revisions in the law. That is, regardless of the wording, the information conveyed can be protected under the "hot news" doctrine.
Note, however, that I'm not an expert in this, and I have not been involved in the AP negotiations, etc.