Not at all and yes, the intent always been there but outside of the RC it was never a stated rule to handle things like that, only implied or called a policy in the Errata.
Indeed, the rule was largely present only through implication and intent. And, of course, through the past behavior of games. But making that information explicit does not strictly imply that the old explicit rule ceases to be. That implication would have to be separately proved, and I can't see any evidence for such a proof.
But now you'll incur a problem of double standards because you want to start arguing that policy or RAI concept gleam from how the books handle them selves should be treated as a rule and it cannot be replaced, ever, because your bias blinds you from treating them equally.
Are you referring to specific versus general or primacy here? In the former case, that's not how these books happen to handle themselves so much as the way all games have worked in the past, to the point where it's just an unstated rule of rule sets. Rules don't even work without that underlying concept in the vast majority of cases. In the latter case, there's obviously no double standard because I'm citing explicit text where there is none for the FAQ.
You can only have one method to handle contradiction, any other rule that attempts to say otherwise would either have to agree or it's self become a contradiction to the other.
Not necessarily the case, and, in fact, not the case here. In particular, the two rules could, and do, handle different sorts of contradictions. If that's the case, then two rules for contradictions could easily exist. I'll go into a lot more detail on how that works in the next part.
But in this case they don't disagree with each other because they are the same things. The RAI concept, Primary/Secondary policy, and the rule about the Order of Rules all handle them selves identically. Outside of exceptions, the primary rule is the most specific rule. It's just one of them simply calls it's self an update that trumps the rest while the others take second place "historical" prizes for not being as clear and laying the groundwork.
They do not handle themselves identically. The order of rules specifically sets forth a hierarchy of rules by specificity, where an individual rule is given an arbitrary specificity label (I say arbitrary because more than three could easily exist, and I could probably point to actual examples of that if necessary), and rules with labels indicating greater specificity get precedence. The proof of this meaning of the text is rather trivial, as I need only note that variations in specificity are always applied directly to the rules. Primacy, meanwhile, doesn't care at all about the specifics of the rule itself and the labels on that rule. It only cares about the source of that rule, and the broad nature of that rule (where, say, the general nature of special attacks gets the same labeling as some specific special attacks). So, under this rule, you give each rule a label, either primary or secondary, based solely on whether the book in question is the primary source for that rule, and primary rules get precedence (I don't think there are more than two primacy labels). Again, this can be easily shown by considering the primary source rule. I mean, it's right there in the title. Primacy modifies source and not rule, and the text supports that reading.
These two rule sets could theoretically be equivalent, were primary sources always more specific or something, but they're not. To show this, just consider some applications. Let's take one we know, the arcane thesis situation, but modify it a bit. In particular, we'll imagine that arcane thesis is in the PHB, with that errata text included, and the text from the FAQ is instead in, I dunno, races of eberron. Neither piece of text is more specific than the other, because each is saying things on the exact same level. "You do get this lower spell level adjustment," is just as specific as, "You don't get this lower spell level adjustment." We're not talking about a specific situation where you lose the lower adjustment, after all. In this case, the PHB, as the primary source, would win. It's a situation which the general/specific rules have absolutely no way to adjudicate, because the specificity labeling is the same.
Next, consider the inverse situation. Human says you have a 30 ft. base movement speed. Fly says you now have this flight speed, contradicting the fact that your only movement speed is that one along the ground. Fly wins, because it's more specific. And, for the sake of argument, and because it's true, we can assume these things are in the same book. The primacy label does nothing, so we must use specificity. Really easy case, that, which speaks to how fundamental this rule is to game design.
Now we must consider a pair of more problematic cases where these rules don't tell you everything you want to know. First, you have the case where specificity and primacy are both equivalent for a pair of contradictory rules. This situation is fundamentally unresolvable, and arguments about such rules usually involve arguing that one such rule is actually more specific. It's a bit difficult to prove identical specificity, but, again, we can consider that arcane thesis situation except with each piece of text in the same book. Notably, this situation only leads to failure in cases where each individual rule would also lead to failure, so it's not like the extra rule is adding ambiguity. Next, we have situations where one rule is more specific and from a secondary source. It's hard to see which resolution rule would win out here from the rules themselves, but looking at how these rules are applied indicates that specificity wins out. After all, a flight spell from any other source would work as well.
So, if specificity is the dominant rule, then why doesn't the FAQ win? Well, simply because the rules aren't actually more specific. This goes back to the FAQ's nature as a source of rulings. Any entry of the FAQ, as a thing describing how a rule works, is necessarily going to be on the same specificity level as the rule it's based on. The FAQ answers aren't saying, "The way the books say it works is correct, except...", they're saying, "Here's how we read this rule." So, in point of fact, if specificity were the only way to resolve rules conflicts, then the FAQ would simply move from unimpactful source to creator of awful ambiguities all over the place. Step backwards, by my reckoning, though you shouldn't take that bad outcome as the core of the argument.
That's my reading of the pair of rules, anyway. It seems self consistent, at least, and I think it also matches up with the rules as they are presented within the books. Which would make it the correct interpretation. And, of course, the self consistency of that reading would at least resolve your claimed contradiction.