In the case where it's actually an auto-fail I may call for a roll anyway. This doesn't apply in cases of 'knowledge' skills, generally, but it may apply in cases where the character is trying to detect a lie from a suspicious NPC, or searching for traps, or similar - cases where the character doesn't know the answer but also doesn't know that he doesn't know the answer. In which case, the die roll serves to provide that uncertainty.
I use dice (and careful attention to the stakes) to resolve uncertainty in the character's fictional action, not to foster uncertainty in the player.
Delericho's comment provoked a similar response in me as it did in iserith.
The uncertainty that I want the dice to foster is not
epistemic uncertainty among the players as to what the GM's backstory is, but rather
metaphysical uncertainty among the whole table as to what the outcomes of play will be.
One stark way to draw the contrast is this: Using dice to keep the story secret from the players is consistent with the game being a total railroad. Whereas using dice in the way that iserith describes - to determine what actually occurs in the fiction as a result of the players' action declarations for their PCs - is antithetical to railroading.
The thing is that I don't find simply examining our hypothetical religious icon (or searching a room, or discerning lies, or many of these other things) interesting in and of themselves anyway. What's interesting is what the PC does with the information, or lack thereof, once that's been resolved.
I tend to agree here with [MENTION=1207]Ristamar[/MENTION] and [MENTION=184]Agamon[/MENTION] - if it's purely random, and the players haven't actually staked anything, then why roll? The GM can just download whatever backstory s/he thinks is interesting and then the players can declare actions in response.
No doubt, as you say in a post after the one I've quoted, the events that result will be different if the players do or don't know the GM's backstory, but what is the point of the player not knowing that backstory?
To me, "I want to roll Religion" lacks the necessary context of the character's goal and approach which makes it easier for the DM to narrate the result of the adventurer's action or to establish uncertainty. The player is effectively saying the action - whatever it is because it's certainty not clear in that offer - is uncertain by default.
Here are a couple of actual play anecdotes that (I think) bear on this.
In the first session of my ongoing Burning Wheel campaign, the action started in the town of Hardby, with the PC wizard Jobe wandering through a market place. Jobe has as one of his Beliefs that he will collect the magical antecedents necessary to enchant an item to defeat his Balrog-possessed brother, and so Jobe's player asked if he could see any antecedents on sale in the market. I described a peddler selling various trinkets and curios, including a golden feather that the peddler claimed to be an angel feather. As Jobe haggled with the peddler over the price of the feather, Jobe's player declared an Aura Reading check to determine whether or not the feather was what the peddler claimed. The check failed - and so Jobe realised that the feather was an angel feather, but also that it had some sort of curse upon it.
The stakes were not expressly set prior to the roll, but I knew what the player wanted for his PC - an angel feather - and the curse was an easily-introduced consequence for failed Aura Reading, and
drove much of the fiction for the rest of the session.
In my most recent 4e session, the players were debating whether or not to destroy the Wand of Orcus - the plan of the invoker/wizard was to merge his conjured Eye of the Sun (which prior events had already established was channelling the power of Pelor) with the Sphere of Annihilation that was hovering on the battlefield to create an almighty engine of destruction, and then roll said enging of destruction over the Wand. The paladin of the Raven Queen was questioning this course of action, and the player of that paladin was wanting to make a Religion check to get advice from his god as to what he should do. But it took a lot of effort for me to get the player to actually convey what it was that he wanted as an outcome from the check, even when I made it clear that I wasn't just going to decide, via GM fiat, whether or not this powerful NPC approved of the other player's plan to destroy the Wand.
In the end some desired outcome was established (I can't remember the details, but the bottom line was that the invoker/wizard was wrong in his plan - the broad background is the rivalry between the Raven Queen and all the other gods), but the paladin player's check failed. I narrated the consequence being one of inadvertently activating the Sphere so that it rolled over him rather than the wand, doing its 6d10 damage plus ongoing 40.