ATLDave is correct in part but incorrect in part regarding judicial activism. In general, you have to take the sum total of the judge's actions in a variety of cases to determine whether they favor judicial restraint versus activism--not one decision. The concept as used by legal scholars really refers to a judge's general temperament and tendencies rather than one particular decision. Restraint also has a whole additional grouping of attributes, for example restrictive sense of standing, avoiding constitutional questions if possible, mootness, jurisdiction, and so on. It really only makes sense to apply the descriptor to a judge's general behavior than one particular decision.
Where it gets difficult is that a judge who ignores a higher law that prohibits an action, such as the Constitution, for deferring to the popular legislation of the moment is really shirking their duty as stated in Marbury. Otherwise, there is no principled argument for judicial review if it is the sort where the judge ratifies the policies that they like as constitutional but strikes down those that they dislike.
You are correct that a judge's overall level of judicial restraint is best assessed by looking at the totality of his or her jurisprudence, and an approach of deciding on the narrowest ground possible is often an aspect of restraint. Still, a judge can exercise restraint in one case but not in another. Not all judges are perfectly consistent - in fact, few are. And judicial scholars have
often written of a particular jurist's restraint in one case or another. I disagree completely that one cannot characterize a single decision as exercising restraint or a more active approach.
As to the rest, I think you are close to conflating
correctness of decision with activism/restraint. Again, many lay people have tried to mush the two together into a single concept, which basically boils down to this: the person has a view of what the constitution means, requires, and/or permits, and any judge who rules in a manner inconsistent with that view is an "activist." There are people on the left who do precisely the same thing and use precisely the same wording. But restraint is not, in and of itself, either left or right. It is an orthogonal axis. There are leftist judicial activists and left-leaning practitioners of judicial restraint. And right-leaning judges of both types, too. All 4 quadrants have a fair number of judges in them.
I'd also note that the most thorough-going/extreme view of judicial restraint would call
Marbury the original activist decision. There is no
explicit grant of authority in the Constitution for the Supreme Court to sit as an arbiter of whether Congress - a co-equal branch of government - has violated the constitution. It is there by logical implication, ruled the
Marbury court, and everyone has been largely agreeing ever since. However, when I was in law school, it was fashionable for a certain segment of the right-leaning scholars and students, chafing under what was the still-recent memory of the Warren court, to call that into question. Newt Gingrich posited that Congress could, and perhaps should, take away the jurisdictional authority for the Supreme Court to even hear such challenges. But around the same time, the Court started striking down some positive enactments that the left had favored, and the value of having an institution to call balls-and-strikes on the conformity of statutes to the constitution became apparent to the right pretty quickly!
To circle back to the actual topic of this thread: The case was decided in a way that comported with the narrow precedent from within the judge's circuit, but against the reasoning of the relevant Supreme Court precedent and against its interpretation of the relevant constitutional provision. This wasn't an "activist" decision, just a lazy and/or wrong-headed one. Now, if the same judge were to strike down, say, a "stand your ground" law on some substantive constitutional ground, or a state-level law preempting local ordinances, that probably
would be fairly characterized as "activist."