I don't agree with this claim. It depends on the nature of the decision procedure.
If your claim were true, just to give one example, a judge could never decide a matter putting to one side information that ought not to have been presented but nevertheless was, and hence had to be excluded. Yet judges do this all the time. Perhaps in some cases they are deluding themselves, but I don't think they are in all cases. Because they have relatively robust decision procedures that rely on certain relevant considerations and which can be applied in disregard of irrelevant considerations even if those happen to be known.
When information so determined becomes to great, or too inextricable, cases are dismissed or mistrials are declared. Further, the judge is operating under a relatively codified set of instructions they do not have the luxury of ignoring. This isn't the case for leisure activities like RPGs that have no such decision requirements. If you're postulating that RPGs have codified decision-making processes for choosing player action declarations, I'd like to see it. Otherwise, it's the player making such choices, and they do so with their knowledge, and so their choice of decision making process is informed by that knowledge, just like the judge's choice to exclude or include information in their decision process is informed by actually having that knowledge.
I don't agree with this either. Suppose a player has a standard decision procedure for dealing with weapon-resistant monsters then s/he could apply that. It's just that, in my experience - yours of course may be different - few or no players have such standard decision procedures. Rather, they intuit and guess - and that can't be done in disregard of the knowledge of the answer.
Continuing with the standard procedure need not be, and in my experience typically is not, informed by the other knowledge. If it's the standard procedure then one just follows it on its own terms.
Really? Let's use a simple procedure for choosing which passage to take in a dungeon. "Always go left." Let's say you're at a T-junction, low on health, and the left hand passage has a scrawled sign saying "dragon," it smells of dragon, you see deep claw marks in the floor as if from a dragon, you hear dragon-ish sounds and roars, and you see flashes of light as if from huge exhalations of flame. Meanwhile, the right passage has a sign saying "exit", you smell fresh air, see light akin to daylight, and feel a clean wind from that passage.
It seems that choosing to use the standard operating procedure must be informed by other knowledge, here. Using it as if you have no other knowledge is impossible -- you're choosing to do so in spite of that other knowledge, not in absence of it. That you can use it like this has never, ever, been the point of anyone.
The second sentence is true. The first I disagree with. Some decision procedures can be applied without having regard to the secret/"metagame" knowledge, and the decision to use them can likewise be made without having regard to that knowledge.
The clearest example I know of in RPG play is blind declaration initiative systems. At the moment of taking the action the player applies a very simple decision procedure - do whatever it is I wrote down in the blind declaration phase - which can be done without regard to the new "metagame" knowledge of others' declarations.
As noted by
@Charlaquin, you're making a declaration absent knowledge, here, not with knowledge. Being held to a decision you made absent knowledge after knowledge has been revealed is a different argument altogether -- you did not decide with knowledge.
The sort of procedure that
@Mistwell has suggested is not the same as bind declaration initiative but it has some resemblance. Again, in my experience at least, players don't have relevantly similar procedures for deciding how to attack creatures that are immune to their normal attack forms.
It lacks resemblance because, in a blind declaration situation you're making a choice absent knowledge that will be shortly revealed. In
@Mistwell's argument, you're choosing a resolution mechanic to arbitrarily decide what action declarations the players make because of the knowledge you have. This is night and day for the topic at hand. Again, the point isn't that you can't choose an arbitrary decision mechanic, but that the choice of mechanic is inextricably tied to what knowledge you do have.
I think there's a bit of ends justifying means here, at least in the sense that you're arguing that you can achieve the same outcome regardless of knowledge if you select the same resolution mechanic. IE, if, without knowledge, I'd roll a die to decide and, having knowledge, I choose to still roll a die to decide so the outcomes are the same. But this isn't the argument being made -- the point of RPGs is that players get to decide their action declarations with respect to their goals in the game. If you have knowledge that directly impacts the decision, you cannot then decide without reference to that knowledge -- however you choose it's due to your knowledge. This is fundamental human nature and unavoidable.
Now, specifically, the point isn't that you always use an arbitrary decision mechanic --
@Mistwell never advanced this idea. Instead, the issue isn't whether you use knowledge to make choices, but what you should do if the knowledge you have is considered improperly obtained. My argument is that, absent bad-faith play where you're engaged in lying by omission or commission, the DM's position as primary author of the fiction means that such 'improper' determinations are entirely in their hands. As such, forcing players to use arbitrary decision mechanics in the face of have knowledge otherwise is a choice forced by the DM, and entirely avoidable. That such arbitrary decision mechanics exist is trivially associated to my point. That arbitrary decision mechanics can be used absent or with knowledge is trivially associated to my point. The point I've made is that choosing to use such measures solely to correct for a choice the DM has made about the nature of the fiction is entirely upon the DM. The point I've also made is that such a choice of arbitrary decision mechanic just to suit the DM is made entirely dependently upon the presence of knowledge judged by the DM to be "improper." It cannot be made otherwise and still be germane to the topic.
EDIT: Speaking purely for myself, I would find a troll encounter where I'm expected to pretend to guess a viable attack mode very tedious. Whereas handling this sort of situation in the way Mistwell has suggested, while probably not my first choice, wouldn't bother me. We as players just keep doing our thing, and engage whatever situations that leads the GM to present to us.
I find this statement interesting. I've previously understood you to not like to play heavily GM directed games because you enjoy having a say in the resulting fiction. Yet, here, you claim that you would not be bothered by the GM directing you into an arbitrary decision mechanic just to support the GM's preferred version of the fiction. I find it hard to reconcile these two statements, and I wonder which one I've misinterpreted.