Seth can't get his new business venture onto the front page of the NYT by himself, after all -- he needs your legal department to make that happen. The rest of the Fortune 500 will promptly DDOS his order takers with their credit card numbers when that gets published. He'll also collect tens of thousands of links, many of them from authority sites such as TechCrunch, Slashdot, Consumerist, the newspapers which take direction from the NYT, etc etc, and as a result rank much better for other brands than he had previously.
If they're stupid, hopefully they're not so stupid that they'll ignore the lawyers who will say there is not even a scintilla of a case.
[Edit: Its not letting me respond because the site is worried I'm flaming you, which is totally not my intent.
In sum, litigation is a last-resort dispute resolution mechanism which you use to achieve business goals. Litigation here will not achieve business goals. On a totally separate level, which is academically interesting but only that, BigCo would be unlikely to prevail with a claim of trademark infringement.
There is no danger of confusion between Ford and Ford In Public -- it says "unofficial", prominently. There is no cognizable commercial damage -- Seth is not trying to sell cars. If you were a particularly bad trademark lawyer, you might argue that someone saying bad things about your brand causes you damage, but that cuts against a finding of trademark infringement, because it tends to demonstrate that the mark is being used, take your pick, transformatively, for identification ("nominative use"), and for purposes of commentary.
But, again, first rule of law for programmers: law is not program code, and litigation is not executing an algorithm. It is a negotiating tactic.]