Eventually, Justice Anthony M. Kennedy broke in to ask his own question, but not before tossing a grenade Sotomayor's way.
"Well, in this case I didn't go beyond the record to look on the internet because I don't think we should do that, but I do have a hypothetical," Kennedy said, harrumphing.
Cue said internet.
Kennedy insinuated that Sotomayor had violated some universally accepted Supreme Court procedure by invoking facts found outside the record. But the rule seems to be that justices don't like other justices doing such research.
As soon as the transcript of the proceedings hit the digital world Tuesday afternoon, the internet was filled with remembrances of other justices - including Kennedy - doing research similar to Sotomayor's.
The first that came to mind for many was Chief Justice John Roberts Jr., questioning a lawyer in 2011 about an Arizona law, the Arizona Citizens Clean Elections Act, that provided public funds for political candidates.
"Well, I checked the Citizens Clean Elections Commission website this morning," Roberts said, with a Perry Mason tone, and what he found seemed to be at odds with Supreme Court precedent and what the lawyer defending the law was representing.
"Why isn't that clear evidence that it's unconstitutional?" Roberts asked of the website's representation. Roberts later wrote the 5-to-4 decision in Arizona Free Enterprise Club's Freedom Club PAC v. Bennett that said the law indeed was unconstitutional.
That wasn't all. What about that time, others recalled, when the late Justice Antonin Scalia included in a dissent in an immigration case a remark made by President Barack Obama only days earlier? The cited source was a newspaper article.
Then there was the time Scalia criticized Justice Samuel Alito Jr. for including his own research about violent video games in a dissent from the court's decision in 2011 striking down a California law that restricted minors from buying such games.
"Justice Alito has done considerable independent research to identify video games in which 'the violence is astounding. Victims are dismembered, decapitated, disemboweled, set on fire, and chopped into little pieces. ... Blood gushes, splatters, and pools.' Justice Alito recounts all these disgusting video games in order to disgust us - but disgust is not a valid basis for restricting expression," Scalia wrote.
And really, one need not look that far back to find other examples. During that same argument last week in National Institute of Family and Life Advocates v. Becerra, a federal-court case, Alito asked about some statistics found in an amicus brief in a similar case in California state court.
"I understand we're speaking outside of the record here, but that amici's evidence in the state court ... was off by, I think, a factor of 10," replied California Deputy Solicitor General Joshua A. Klein.
There is a lively debate about whether and when justices should consult facts outside the record, which have not been subjected to the kind of adversarial scrutiny applied to facts in the record.
"I think there are good reasons why appellate courts, including the Supreme Court, generally shouldn't consider facts outside the record," said Leah Litman, a law professor at the University of California at Irvine. "But there are also times where it would be difficult not to do so, particularly when they are confronted with particularly credible evidence ... that is relevant to a case or potentially undermines one of the premises on which the case is being litigated."
Sotomayor was looking at the website of the antiabortion Fallbrook Pregnancy Resource Center, an unlicensed clinic that brought one of the suits against California's requirement that it disclose, in as many as 13 languages, that it did not have medical personnel on staff.
Sotomayor noted the website showed a woman who appeared to be a nurse standing by an ultrasound machine in an exam room. It promised medical information on different abortion procedures, even though it does not offer them.
"If you're an unlicensed facility, about pregnancy, why shouldn't you tell people that you're not a doctor?" Sotomayor asked Michael Farris, who was representing the clinics.
Allison Orr Larsen, a professor at William & Mary Law School, has written about the concerns that accompany justices doing their own research, as well as relying on facts presented in amicus briefs that also have not been subjected to the adversarial process.
Larsen analyzed 15 years of Supreme Court decisions for a study she produced in 2012 that found more than 100 examples of asserted facts from authorities never mentioned in any of the briefs in the case.
But she thinks it makes a difference in this case that both California and the challengers had referenced Fallbrook's website in their merits briefs.
"Some may say that there is a distinction between citations in the briefs and evidence in the record, but to me the critical question should be whether the issue was put to the test in the adversarial process," Larsen said in an email.
"If the parties both had a chance to weigh in about what the websites actually said or didn't say (and if they could respond to each other in briefs), then that should assuage concerns about tainting judicial opinions with untested and potentially unreliable factual claims."
Larsen remembered another justice who relied on data outside the record: Kennedy.
In his opinion in Graham v. Florida, in which the court invalidated life sentences without parole for juveniles who commit non-homicide offenses. Kennedy cited a letter from the Bureau of Prisons, solicited at his request by the Supreme Court Library, about the number of such prisoners.
After the decision, the government submitted a letter to the court saying the research had been wrong.