Did you even read Sotomayor’ dissent? I did.

You are not considering the part where we can’t use relevant testimony or documents to prove that what the President does is illegal in the first place. The President can just say whatever illegal things they did were official acts, and all the evidence that might prove otherwise is off-limits. It relies on other people in the administration to not follow the illegal order, but of course that is a weak protection and the President can fire them or do something illegal to them without consequence too.