That aspect involves the FACTS in a court case, after the initial determination of that case is decided. In the initial case, the facts are of paramount importance.
Afterwards, it's a different story. For example, in a murder case, the facts are placed in evidence, their importance is argued, and they are the at the core of the decision to convict, or not. In the appeal, the facts are totally unimportant. In an appeal, the lawyers focus on the PROCEDURES of the case - did everybody follow the RULES of the trial, did the accused have his/RIGHTS constitutionally protected, did the PROCESS fit within the guidelines?
Whether the accused is actually INNOCENT is beside the point. So, in our system of justice, it's not only possible, but actually OK to overturn the conviction of a guilty person, and uphold the sentence of an innocent person.
Civil cases work the same way. After the initial determination, don't dispute the facts, argue the WAY the court handled the PROCESS.
And that's the problem with the Schiavo case. The facts about her condition make her ineligible to die. But the process condemns her to death.
Andrew C. McCarthy has a post on the National Review site that explains this very well.
the question that impelled the extraordinary intervention of Congress and the president over the weekend. And that is the question that U.S. District Judge James D. Whittemore refused to entertain in rejecting, early Tuesday morning, a request to reinsert Terri Schiavo’s feeding tube. Thus, her excruciating march to death by starvation and dehydration continues.
In 1990, in a case called Cruzan v. Missouri, the U.S. Supreme Court assumed that a competent person would have a constitutionally protected right to refuse lifesaving hydration and nutrition, and held that where a person (a) was actually in a persistent vegetative state (PVS) and (b) had actually evinced a desire not to be sustained in that state (i.e., a desire to die rather than be kept alive), the state was permitted — but not required — to allow her surrogates to discontinue sustenance.
Cruzan is distinguishable from Terri Schiavo’s case in that there is powerful reason to doubt that Terri is in a PVS.