Actually the Constitution gives Congress the authority to limit or broaden the appellate power of the federal courts.
Had the Schindlers actually asked for a de novo trial, it would have been interesting to see what would have happened.
Exactly, while limiting the courts to deciding on the Constitutionality of laws as enforced by the executive branch. Gig 'Em
Art III, Section 2, Clause 2:In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact, with such Exceptions, and under such Regulations as the Congress shall make.
According to findlaw, no one is sure whether Congress has the power you are arguing:
There thus remains a measure of doubt that Congress' power over the federal courts is as plenary as some of the Court's language suggests it is. Congress has a vast amount of discretion in conferring and withdrawing and structuring the original and appellate jurisdiction of the inferior federal courts and the appellate jurisdiction of the Supreme Court; so much is clear from the practice since 1789 and the holdings of many Court decisions. That its power extends to accomplishing by means of its control over jurisdiction actions which it could not do directly by substantive enactment is by no means clear from the text of the Constitution nor from the cases.
It's a pity that the Supreme Court didn't take the Schiavo case. It could have cleared up this legal question on Art 3, Sec. 2, Clause 2 (second half).