The facts of the litigants don't matter to the legal reasoning, because SCOTUS decides matters of law, not fact.
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.
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).
That doesn't describe Scalia at all. Scalia applied originalism when it suited him, and abandoned it when it interfered with his ideological goals.
Scalia like most SCOTUS justices, cared little for the actual litigants, since they were largely irrelevant to the matters at hand other than as vessels for bringing the matter to court. Due to the length of time it takes cases to get to the Supreme Court, many of the named litigants aren't even the original parties, the original parties having long since died or left office.