I don't think so. Certain things are disallowed by US law (e.g. bribery) but I don't think labor standards are dictated much if at all. The ILO though may have something to say on the matter. "If not, what is it about a US corporation that makes it a US corporation? -especially one that does most of its manufacturing overseas?" As far as I know, its related to things like taxes, where the head corporate office is, etc... Also, its worth mentioning that this issue is one of jurisdiction, not rights. AFAIK, the court decided that it has the jurisdiction to hear cases against companies by foreign citizens for actions that occurred abroad. Prior to this it had been agreed that this could be done against individuals but the districts disagree on weather it can be done against companies (though recently the 7th circuit has also agreed it can be done against companies: http://www.ca7.uscourts.gov/tmp/9H0ZPPY9.pdf). The question of what rights can be enforced (or, if you prefer, what actions can be punished) is a separate one that will be answered by looking at treaties, customary international law, etc... (http://en.wikipedia.org/wiki/Sources_of_international_law). If you get a chance to read it you should, its a short well written opinion. If you look at the 7th circuit opinion I linked to, you'll see that Judge Posner says that 1) they have jurisdiction but 2) that the alleged actions are not a violation of international law. In fact, he implicitly brings up good reasons not to apply U.S. law. In different countries the economic situation is different. It may not make sense to impose the kind of labor limitations we do in the U.S. since it may do more harm than good.
Thanks. I read it. I didn't understand all of it, I am sure; but it was interesting. And I just now read that Firestone decision through. It does make a convincing argument. Of course, we cannot simple wish that one place was like another and then set laws that assume it. So here is an interesting question: What if the residency of a corporation was determined by where it had the most employees? To me, it's interesting that Firestone argued that: "...conduct by a corporation or any other entity that doesn’t have a heartbeat (we’ll use “corporation” to cover all such entities) can never be a violation of customary international law, no matter how heinous the conduct." And now in the US, we have the rise of corporate personhood regarding campaign financing. Maybe corporate residence should reflect more than where they take their mail?