The lower federal courts are a creation of Congress so under the Constitution they cannot overrule the coequal branch of the executive, only the Supreme Court may do so. I think going forward the only way out of this tyrannical rule of federal and state courts is for the executive branch to ignore all rulings and only defer to those lower court rulings when the Supreme Court rules on the lower court decisions.
Yes I have long said the President does not have to obey these lower court injunctions. Obama ignored the lower court injunction on his drilling ban in the Gulf.