Note that supreme court judges are different from regular judges in how their interpretations are made and how they are applied. For one, AFAIK, they do not hear experts, they are the experts.
You are more correct than you realize.
When SCOTUS is sitting in appellate jurisdiction--as is nearly always the case--it's not there to hear the facts of the case. Facts are developed and judged at the trial level. Appellate courts don't judge facts, they judge law: was the evidence properly admitted/suppressed under the Rules of Evidence and relevant caselaw? Were there procedural errors in the handling of the case? Is there a constitutional issue making a statute invalid, or making an interpretation invalid? Was a statute used in a manner contrary to previous use without a good reason for the divergence from established jurisprudence?
The appellate court judges are experts on the law; it's not up to them to decide the accuracy and weight of the facts, just to decide whether the trial court followed the established law in getting to the result it reached. If you read most appellate court decisions, they rarely change the outcome of the trial court outright, but rather remand the case to the lower court with instructions to hold further proceedings "consistent with this ruling." That is, "y'all messed up on these points, go try again and get those bits right this time." It's not unheard of for the trial court to have new proceedings, make the procedural changes required by the higher court, and still reach the same result.