Well, that is not quite right as far as the procedure goes. First off, it is pretty hard to get a case heard by the Supreme Court (SCOTUS is a traditional abbreviations).

Unless the murder happened under federal jurisdiction, the case would be tried in a state court. If the loopy theist murderer tried to use such a novel legal theory, it would be an admission of guilt and he could be sentenced directly. Then there is a second level where one can appeal a conviction but in order to do that, one must make a different legal argument, specifically that the original court did not follow some established procedure and that the outcome would have been different had that been done.

Since the original legal theory requires an admission of guilt, it is pretty unlikely that the case would even be heard on the state appellate level. The appeals court would probably reject such a petition outright.

In the case of a murder happening under federal jurisdiction, the idea would be pretty much the same except that federal courts have much stricter rules than state courts usually do. So again, it is unlikely that it could be heard on a higher level. Odds are that SCOTUS would never get a crack at such a case.

Then too, even if such a case did make it that far up the legal system, SCOTUS is under no obligation to hear the case. They have broad ability to reject possible cases without even providing a reason to do so. In the scenario that you set up, they probably would not touch it directly because it is something that has never come up before. If it were a death penalty case, they might take it but they would limit themselves to the question of whether the death penalty was in order and they would not consider if the conviction was valid (again, it is one where the legal theory is an admission of guilt).

Even so, the word of SCOTUS is not the final word in the USA. They are not the constitution to all intent and purpose. The system is called checks and balances and it works sort of like the children's game scissor/paper/stone where each of the three branches of the government can overrule the other two at need. So all three branches have an incentive to work together and not just do loopy insane things.

Of course, each branch has gone out on the deep end many times and no doubt will in the future. However, when that happens, they can be reeled in by the other two branches.

They would follow stare decisis first. If a court made a decision, and it appealed up to them...then they would likely just defer back to the lower court.

The only reason I could see them even accepting that kind of thing, is if the alternative put it out of their legal reach. Such as, between another nation's courts and ours. The one thing our court system demands is respect and priority.

Not that that is any diferent from most other courts of law.