It is true that an appellate court will not retry a case. However, one can remand a case back to the lower court from which it came for a new trial. This remedy is rare. Heck, winning on appeal is quite rare if the case was originally heard by a competent judge. And even incompetent judges tend to get competent in a hurry -- they don't want to see a lot of their cases get overturned on appeal as that looks horrible come election time.