Koranot, thank you for your posts as it gave me an opportunity to revisit my arguments and readdress any potential criticism/weaknesses in them. As I understand your posts, there are two basic criticisms with my arguments: (1) you try to illustrate how there is a conflict between Predatory Fighter and Supporting Attacks, therefore "AB>BRB;" and, (2) then you try to point out how it is an error to make a distinction between regular close combat attacks and Supporting Attacks. Unfortunately, both of your rebuttals are actually guilty of the same logical fallacies and faulty reasoning I pointed out in my initial post but I'll go a step further to illustrate in this post why.
In-case this post is TLDR again, simply go down to the "conclusion" and see an abbreviated version of what I say to Karanot's points and why and if you still disagree with me, read my arguments as I walk you through why I am ultimately right and how.
Anyway, moving on, I'll start with the second criticism first since it is shorter. I do not create an "artificial difference" between Supporting Attacks and regular close combat attacks...The BRB creates an actual difference when it differentiates between how close combat attacks for models in base contact work and how close combat attacks for models not in base contact work. Therefore, if you are in the second rank, you can only attack using the Supporting Attacks method and are making what the BRB refers to as Supporting Attacks (BRB itself says "[w]e refer to the attacks made by these models as supporting attacks"). Therefore, when it says "Attack" in the Predatory Fighter rule, is it a Supporting Attack or a regular CC attack? If so, how do you know? The rule is badly worded but absent clearer language you should interpret a vague rule as conservatively as possible rather than liberally to get a benefit based on the vagueness of a rule. Also, when you use Murderous Prowess as an example, you fail to take into account that Murderous Prowess specifically says "Close Combat Attacks" rather than just "Attack" as the PF rule says. That difference might be significant, it might not, however, my ultimate point was that what rule was anyone using to say they can make more than one Supporting Attack per CC phase? Absent language in a rule that says "despite normally being able to make a single Supporting Attack" or something to overcome that restriction. Indeed, there is no indication that Predatory Fighter says it works with Supporting Attacks at all which is troubling and plays into how I address your first criticism below as the whole crux of the debate hinges on if there is or is not a conflict.
Regarding the first criticism, the "conflict," as you use the word, arises between the two rules because one rule says "make an additional attack" and another says "you can only ever make a single attack" and you assume that this is the kind of "conflict" that means "AB>BRB." You fail to realize, however, that this is a false equivocation fallacy because you are not using the word "conflict" in the same sense and way or context the BRB does and you are not applying the rules appropriately in light of what they actually say. Therefore, before anyone starts throwing around the "conflict exists, therefore AB>BRB" card, they need to define and understand their terms, otherwise I end up arguing about an orange at store X while you end up arguing about an Orange at store Y which is hardly conducive to a meaningful logical discussion.
So with that said, lets be clear that we *are* talking about the kind of "conflict" as explained and applied in the BRB. Indeed, to find out what anyone means when they are talking about "conflict" in this debate, we must look at the example and language from the BRB regarding Basic rules and Advanced rules, then we must apply them in the proper context because that is where the "AB>BRB" rule is.
Basic rules "apply to all models in the game, unless specifically stated otherwise" while Advanced rules "apply to specific types of model, whether because they [are different/have different rules]...The advanced rules that apply to a unit are indicated in the entry for the unit in their relevant Warhammer Armies book."
Furthermore, under the Basic Versus Advanced rules it says, "where rules apply to a specific model, they always override any contradicting basic rules. For example, the basic rules state that a model must take a Panic test under certain situations. If, however, that model has the rule that makes it immune to Panic, then it does not test for Panic- the advanced rule takes precedence."
Therefore, we must look at the types of rules that are allegedly conflicting and more specifically, how they are conflicting. Indeed, the type of conflict we are dealing with here is where an Advanced rule in an Army book is in conflict with a Basic rule in the BRB such that they grant/deny the ability to do something with equal force of language so that they cancel out resulting in an absurd result. I say "with equal force of language such that they cancel out" because in the example in the BRB, one rule says "in x circumstance, take a Panic test" while the other rule effectively says "in x circumstance don't take a Panic test". To clarify, a unit with the "immune to Panic" rule automatically passes Panic tests" and therefore, if you automatically pass a particular test, you obviously need not take the test as regardless of the result, (i.e., a double 6, which normally always failed, is rolled) the test is still considered to be passed and so the rules cancel out and the Advanced rule take precedence.
Ultimately, the way the two rules conflict is key here as illustrated in the BRB as even though Supporting Attacks is a Basic rule (since it is not included in a unit's entry), the way it conflicts is what makes AB>BRB or not, not the simple fact that it conflicts at all. Specifically, if Supporting Attacks only said "when making supporting attacks, a model only ever makes a single attack" then it would be a contradiction/conflict (as per the "AB>BRB" clause). However, that is not what we have going on here. Here, we have additional language in the Supporting Attack rule that specifically says "regardless of any special rules." Therefore, the focus and analysis shifts from the "make an extra attack" versus "no extra attack" portion of the rules to "regardless of any special rules" versus "regardless of any limitations" language.
Do you see that? This isn't a situation where it is Rock Paper Scissors and both rules pick Rock and cancel out therefore AB>BRB, this is a situation where one rule has Rock (Supporting Attacks) and another has Scissors (Predatory Fighter) because of the additional language in the supporting attack rule.
To put it into simpler terms, we have the quoted rules as follows:
SA: "(1) only ever make a single attack, (2) regardless of any special rules"
PF: "(1) make an additional attack"
If the "(1)" part of each rule cancels out, and if those are the only parts of the rule, then I concede, absolutely, PF>SA. However, once the "(1)" part of each rule cancels out, the "(2)" part of the SA rule remains and there is nothing in the PF rule to cancel it out, therefore it remains effective.
Conclusion:
In conclusion, while there are parts of PF and SA that contradict and cancel out (i.e., the only 1 attack versus gain an additional attack), not EVERY part that is relevant does (i.e., SA has language that says "regardless of any special rules" while PF does not have any equivalent and contrary language), and therefore, the part that is not canceled out remains effective. It works like this in math too....
x+y=x
-The left part of the math equation is the SA rule while the right part of the math equation is the PF rule.
-The x is the part of the SA rule that says "only 1 attack ever" while the y part is the one that says "regardless of special rules ever." The x part of the PF rule that says "gain an extra attack."
Now if you were to solve this math problem, you would end up with the "Xs" cancelling out and therefore that part of the rule that remains is not in conflict with a part of the PF rule in the sense and it works out...If you are making a supporting attack, you cannot benefit from the predatory fighter rule's extra attack.
In order to have a conflict that creates an "AB>BRB" conflict, you would need to have language in the Predatory Fighter rule that said something like "regardless of any restrictions" or "even when making Supporting Attacks." THEN and ONLY then would the two rules truly contradict each other and therefore in that and only that situation would AB>BRB.
FYI, if someone wants to argue that PF works where Frenzy does not because of how the rules function, they are guilty of making the logical errors in my first point in my original post (i.e., SA makes no distinction as to how the extra attacks are added, only that they are added by a special rule).
It's sad though, considering how very little faith I have in them getting a FAQ out for us. Seeing as how they are fixing WE/End Times books that came out much later than ours... Ugh... 
