The Oberoni Fallacy- There is no inconsistency/loophole/mechanics issue with Rule X, because you can always Rule 0 the inconsistency/loophole/mechanics issue.
This one is more difficult, and requires a little more unpacking. Let's start by simplifying it and rewording it. There is no PROBLEM with Rule X, because you can always FIX the PROBLEM.
All I've done is simplify the language regarding issues to "PROBLEM" and change Rule 0 to "FIX." Should be pretty uncontroversial. When you've done that, it becomes easier to see the actual issues with this so-called fallacy. First, people would have to agree that there is a problem- this is often the crux of most conversations, which is ignored. One person's problem isn't another person's. But let's assume there is agreement that there is a problem! So you can take the statement literally- "There was never any problem, because you can always fix the problem." Well, that's an absurd statement! "My car's bumper doesn't have a problem, because I duct taped it into place," doesn't mean that there was never a problem with bumper.
But let's turn this around a little; RPGs are, by their very nature, incomplete systems. To the extent that there is a Rule 0 (or similar mechanism for adjudication or modification), that is part of the rules, and changes made pursuant to it are also part of the rules. There will always be room for adjudication. And the norms and expectations in RPGs assume that people will continue to "make games their own," through modification, use of 3PP, and homebrew, or even the creation of their own systems. More simply, RPGs are not cars. When people are having a discussion, they are saying, quite simply, "I don't have an issue with Rule X, because I do this." So to tell them that there is a problem, one that they do not have, is also incorrect.
In more concrete terms for RPGs, we can look at how it applies in two different contexts-
A. Defining the problem. Take the martial/caster debate. PLEASE. Ahem. So, person A says that the martial/caster divide is a problem with 5e. However, that isn't something that is universally agreed-upon. Just because one person believes something to be "a problem" in the rules, doesn't make it so. If person B suggests a way to fix it for person A, then that still doesn't mean that this is "A PROBLEM," it just means that someone is suggesting a fix for person A.
B. Actual rules problems. In AD&D, the PHB stated that Monks attack as thieves. The DMG has them attack as Clerics. This is an actual rule problem- an inconsistency. While there is a "correct" answer (clerics, Sage Advice #31), saying that you could Rule 0 the correct answer doesn't actually get rid of the fact that there was a written issue in the rules.
Generally, though, the problem with this so-called fallacy is that people aren't discussing actual rules inconsistencies, so much as trying to shut down people who are offering their advice with dealing with specific issues. On a higher level, the Oberoni Fallacy isn't a fallacy, it's simply a statement as to the philosophical approach one takes to gaming; one might as well say, to coin a phrase, "Rules, not rulings."