Your question highlights a real problem
In principle, necessity and brute facts are two very different things. Necessity means that one can derive the condition from logical principles, and these principles explain the circumstance. Brute facts are the first leg of Munchausen’s Trilemma. A second leg is to pursue the infinite series of causes. This is the leg that science assumes, and works to understand. Necessity is a possible answer on this leg. Brute fact, involves the abandonment of the pursuit of the infinite series of causes, with the claim that something just IS.
Therefore necessity and brute fact, in principle, are very different.
However, philosophic practice is poor in using necessity
Your question identifies a major failing in philosophical practice relative to necessity. And that is to treat necessity as if you can POSTULATE it, rather than having to PROVE it.
A necessity claim has to be demonstrated logically. Which Oppy did not do. Without any justification, he is just mislabeling and rebadging his brute fact assumption, and abandonment of methodological naturalism, by invalidly pasting an unjustified claim of necessity on it.
This is a common problem in modal thinking in philosophy, where incoherent and unsupported claims of “necessity” abound.
Theologians used this bogus necessity trick first
Before dissing atheist philosophers though, theologians have a similar problem. Classical theism provides little to no justification for a God being a “necessary” being. As with Oppy, this claim is usually treated as an unsupported (hence brute fact) postulate.
Necessity claims fail to sole the Trilemma
The problem for the “necessity” solution on the infinite series leg of the Trilemma, is one can ask for the justification of even a thorough spelled out logic derivation, and eventually show that the assumptions behind it have not themselves been justified. This is the case for logic, which is not self justified.
Worse, logic theory has established there are infinite logics, and they reach different conclusions. One CANNOT validly show a necessity claim is valid across all universes, as those universes could, by contingency, operate by different logics.
There is another leg to Munchausen, and that is circularity
One can try to get around the other two legs by identifying a complex web of assumptions, and try to at least show they are a validly coherent set. This is the third leg, and it is not and cannot be “necessary” as there are potentially infinite assumption sets one could postulate.
One could postulate a logic system, derive a necessary universe from it, derive our universe from those properties of the necessary conditions, and then show internal consistency by deriving down to show consistency with all of science, and integrating up from science to show consistency with the assumption set.
It takes a lot of work to show one has a fully coherent model of how our universe came to be, and Oppy has not done that. And given how our current science is pretty radically incoherent (empiricism does that, multiple bottom up inferences tend to produce incompatible predictions, and ours do), Oppy CANNOT do this.
And even if he did, all he could claim is that this is one possible worldview of potentially many other such coherent worldviews. Which is NOT a strong enough position to claim atheism from.
Note also, the name of the Trilemma was chosen to ridicule the coherentist leg. It is from a fairy tale about Baron Von Munchausen. He was out riding, and his horse got stuck in mud. The horse could not get itself out, and the Baron could not lift it out. But by making a circular logic loop, where he got in the saddle, and grabbed and lifted on his own ponytail, he was able to lift his horse through his stirrups. Make a circle large and complex enough, and one can accomplish the impossible with it!
At any rate, coherentist circularity is at least one possible answer, but one that neither Oppy nor his theologian rivals have actually presented a valid example of.