Yeah, I think that's accurate.
These decisions are not intended to be precedential, or really all that big a deal, mostly procedural. But, they have tended to become something else over the last few years.
These stays are supposed to balance the likelihood of winning/being right on the law against the irreparable harm that results if they are wrong on the law. So a high likelihood of winning "trumps" great harm, while great harm can outweigh a shakier case.
One kind of unusual thing recently is that the Court has recognized the harm that results to people if they are deported without due process. That harm is so great that even if the government is right, they're gonna stay it because of the harm. That sort of factual sensitivity is actually somewhat unusual from the Supreme Court, especially this one.
Jackson basically concedes that the government is going to win this on the merits, but argues that the harm is so great that the district court decision should remain intact until the government pretty inevitably wins. A great humanitarian position, but I'm not sure such a great one on the law itself.
The simple fact of this is that these parole programs are created by fiat and can be ended by fiat. That's one of the several flaws in our immigration laws. Raises the question whether the Supreme Court should correct or mitigate all wrongs or just the ones that rise to the level of violating the constitution.