This is how I read it also. The plaintif was trying to show that the ATF's failure to act was the same as a refusal. It was ruled that it is not the same. I hate to say this, but I believe the ATF is not at fault here. Congress is...
Then, IMO, Thomas should have ruled that, by defunding the ATF to perform this service, Congress basically REMOVED that power from the ATF, and has made a de facto decision for every felon in the country. That would have forced Congress to immediately either fund the program or change the law, giving affected parties a true recourse.
Playing mind games with the Bill of Rights is a horrible idea - this decision could be a recipe for some horrific legislative tyranny if you think about it - Congress can now, for example, require a permit for anyone to run a newspaper, create a review agency, and then deny that agency funding to approve permits. SCOTUS tells a party bringing suit that their case hasn't been heard by the agency, and that is that - no more newspapers. Both the 1st Amendment and 2nd Amendment are fundamental rights, but SCOTUS has shown the way to abridge those rights through legislative catch-22s.
The more I think about it, the more I think this was a really, really bad decision, because it sought judicial purity at the expense of logic - in other words, it was patently absurd.