Not exactly. Congress can re-enact the overturned law with different wording that avoids the court's ruling, or it can pass a "standard of review" statute that directs the courts on the criteria to use in deciding cases. That statute would then require the president's signature.
YEs, you're right but it still does not explain the utter ignorance displayed by this puts.
Because EVEN if your scenario takes place it would NOT BE Cain or any other president who over turned the ruling but Congress!