Yes.
And, here's the problem with this guy's theory. Suppose that California's governing politicians wanted to stifle conservative activists and passed a statute making it a felony for demonstrators to carry signs that espouse conservative opinions. Some conservative activist would file a lawsuit in a federal court arguing that the statute is obviously unconstitutional. And, the federal judge would agree and declare the law unconstitutional.
Now, if this author is correct, then the State of California could just decide not to appeal. Since the district court was not an appellate court, the State of California could just go on enforcing its unconstitutional statute.
But, of course, this author's theory is not correct. The State of California is bound by the decision of the U.S. District Court even though it is not an appellate court. The State of California doesn't have the power to decide which federal courts it will obey.
Yes, but the fact that SCOTUS vacated the ruling of the 9th Circuit means that the ruling of the District Court applies only to the parties to the case, and only in that District. Since California has several Federal Court districts, that would seem to imply that the ruling only impacts a portion of the state.
There is also the question of whether there should be any finding of unconstitutionality at all. Since the state declined to defend the law, the most the plaintiffs should have accomplished is a default judgment on their specific claim. That is why Walker allowed the supporters of Prop. 8 to defend the law in his court - he wanted to have a trial so he could declare the whole law unconstitutional, not just grant a default judgment to the plaintiffs. But if the supporters of the law did not have standing to defend the law at the 9th Circuit, they also did not have standing at the trial court, and the whole decision by Walker should be vacated and replaced with a default judgment.