I don't believe the role of a state of federal appeal court is to decide if a person is innocent or guilty nor if errors were made on either side. The role is to the review trial proceedings and decisions of lower courts to determine if errors were made that were "serious enough" to effect a trial outcome.

I believe the role of the USA Supreme Court is somewhat different (as noted below). So, the comments you refered to by Greg F, could have been be taken out of context.

The USA Supreme Court's Role
""The Court typically will agree to hear a case only when it involves an unusually important legal principle, or when two or more federal appellate courts have interpreted a law differently. There are also a small number of special circumstances in which the Supreme Court is required by law to hear an appeal.""


US Federal courts