Well, the Supreme Court is actually the court of first instance for some types of cases, and decides both matters for those cases. It can also decide matters of fact in some cases, for various reasons.
Those situations aside, I think Sotomayor and Ginsburg's emotional appeals in oral argument are representative of how they are actually deciding those cases (i.e. for reasons related to the specifics of litigants), and that the written opinions may simply be a legal veneer over their true motives.
Well, the Supreme Court is actually the court of first instance for some types of cases, and decides both matters for those cases
It's called "original jurisdiction" and for SCOTUS their scope of original jurisdiction is limited to cases between the states or involving ambassadors or other "public ministers." As a portion of SCOTUS' load, such cases are such a small fraction that it can be decades between such cases.
SCOTUS otherwise does not decide matters of fact because it's not within their jurisdiction to do so as an appellate court. They can overturn lower-court rulings on the facts, but in doing so must remand to the lower courts for new rulings on the facts. Additionally, while they can take facts into account in their rulings, such facts must be part of the record established in the lower courts (i.e., the trial courts), unless it is a case of original jurisdiction for SCOTUS (meaning state vs state cases).
The facts of the litigants don't matter to the legal reasoning, because SCOTUS decides matters of law, not fact.