I don't normally like to weigh in on such matters without thinking them through first, but let's not write this one off too quickly. The key language, it seems to me, is the phrase "subject to the jurisdiction thereof." As the materials in the original post indicate, everyone in the United States, whether here legally or illegally, is in some sense "subject to the jurisdiction thereof." That is, there is a purely territorial element to governmental jurisdiction. If that is the sense in which the Fourteenth Amendment uses the phrase "subject to the jurisdiction thereof," the phrase is utterly pointless. If it means anything else, the most plausible meaning may well be something like "subject to full jurisdiction." On the other hand, it also seems unlikely that only children of citizens are automatically citizens, because it would have been very easy to use the word "citizens" in that context.
The Fourteenth Amendment was a botch-job of major proportions, and this may be one more example of that principle. Bottom line: don't make hasty assumptions in either direction on this point.