I said "don't know, and aren't expected to know". That second clause in my statement is doing work.
What counts as "aren't expected to know" is going to be context sensitive. An example I've discussed in the past, which I don't think counts as "aren't expected to know", is an example skill challenge set-up in the 4e DMG. In that example, there is a NPC who can't be intimidated by the PCs - they have no credible threat to bring against him, and he will just be annoyed at such an attempt. The notes to the set-up state that the players (and their PCs) can learn that the NPC will respond poorly to threats if they make a successful Insight check.
As I said, I don't think that counts as "aren't expected to know", as the information is readily available via a pretty transparent and well-understood mechanic (the Insight check) that can be readily deployed during the course of resolution at relatively low cost/risk to the players. It's the social equivalent of a hidden foe on the battlefield, who is detectable by declaring an appropriate action during combat. It's also comparable to a concealed or secret door in map-based exploration-oriented play - again, that is something learnable by the players, that it is expected they will (or at least are likely to) come to know during the course of their play.
An example that I would contrast with those in my previous two paragraphs is how to make a magic item in 2nd ed AD&D. The player will not know the recipe from the outset, and it is not readily learnable by a fairly straightforward action declaration. The process of discovery is itself likely to take one or more session to play out, is heavily subject to GM fiat at every stage, and will mean that there is a considerable period of play which is not about making the magic item at all, but rather is about doing whatever it is that the GM has deemed necessary to enable the desired play (of making a magic item) to take place.
To relate this to the path A/path B example. If learning what is down Path A vs Path B is about (say) declaring and succeeding at some sort of knowledge or research check that is readily performable in situ or as part of the prep in a preceding downtime phase; or is easily done in situ, say by a single successful Stealth check to scout; or via a successful social interaction with a guardian at the entrance from which A and B fork; then I wouldn't say the players are not expected to know. The knowledge is easily within their grasp, without play detouring off into something wholly different.
But if learning what is down Path A vs Path B is more like the magic item creation example, and (eg) requires the players to have whole other adventures tracking down and dealing with sages, or questing to find ancient maps or journal entries, or something of that sort - action which itself will have stakes and consequences that are quite divorced from the expedition to the dragon's lair - then I think that it's fair to say that the Path A vs Path B distinction isn't that meaningful at all: if the players don't get the information, the choice of which path is essentially arbitrary and so doesn't matter; and if the players set out to obtain the information, they are committing to a different adventure, and so Path A vs Path B has paled into relative insignificance for the moment - the GM would be better off waiting to find out the consequence of that subsequent adventure, and then prepare the dragon's lair scenario down the track to fit in with whatever the fallout of the other, info-quest adventure is.