The case involves the Freedom of Information Act (FOIA), which was passed decades ago and has mounds of decisions on the books interpreting its provisions. This is federal statute and the legal rules concerning statutes center on what the legislative body intended in enacting any given statute. FOIA has 17 categories by which a party can be protected from disclosure, including one for "personal privacy." AT&T's central argument - the centerpiece upon which the lower appellate court decided the case in AT&T's favor and upon which AT&T's counsel was riding hard hoping to gain a victory in the Supreme Court - rested on the idea that Congress, in enacting FOIA, defined the word "person" to include corporations and, hence, when that same Congress, elsewhere in that same statute enacted at the same time, specified that there was a right of "personal" privacy, it must have intended "personal" to include every one listed in the statute as a "person," i.e., corporations.
Basically, after the justices ripped AT&T's counsel apart, Chief Justice Roberts said, in effect, OK, if "personal" derives from "person," let me see if I can think of other cases where an adjective links with its noun counterpart, then let's see, "craft" and "crafty", "squirrel" and "squirrely", "pastor" and "pastoral" and so on - of course, making it look absurd that anyone would argue that some common meaning was intended by Congress simply by the force of the linguistic connection between "person" and "personal." By all accounts, this salvo had a devastating effect, leaving AT&T's counsel stammering about how his client had other arguments upon which to rely beyond the "grammatical imperative."
On the merits, too, this is the same court that, in Citizens United, had found that the idea of corporate "personhood" should be recognized such as to give corporations free speech protections vis-a-vis attempts to limit their speech through campaign finance reform legislation. However (though this is not sufficiently appreciated by those who disdain the idea of corporate personhood), the idea of a corporation as a "legal person" dates back at least to Blackstone in the 1750s and is deeply rooted in the law (http://news.ycombinator.com/item?id=1099625). Legally, it was not that big of a jump to say that the idea extended to protecting the speech of corporations under the First Amendment (of course, the case could have easily gone another way as well but this court had no problem with such a result). The FOIA case, though, is entirely different. Here, Congress enacted a statute with specific purposes and built in protections for "personal privacy" without any hint that this might apply in some nebulous way to corporations. When that statute is examined, it becomes very difficult to justify the idea that Congress would have intended any such result in using the phrase "personal privacy" and the court of appeal had reached that result primarily based on the flawed grammatical argument noted above. That is why the Roberts comments from the bench were so devastating.
The government's counsel, sensing a good thing, waived the last 10 minutes of time for rebuttal and was more than content to let the matter rest when his turn came. When a lawyer voluntarily decides to shut up, you know that something major has just happened!
All in all, a really bad day for AT&T's lawyers and for its case.