Maxperson
Morkus from Orkus
Forcing me to roll the check isn't playing my character, though. Making a knowledge check isn't about something my character does in the fiction. It's about establishing backstory.
The DM has decided to step into your character and determine what he knows and why. That's playing my character. That it is dependent on a check doesn't change that he is forcing my character to take an action that that I the player am against. Again, that's playing my character. He can't do that.
Suppose the question was not about the formula for the phasing potion, but the location of the chief alchemist's office. Again, I the player have no idea (we've never even used a map of the college, as it's just something that comes up during downtime), but surely my PC at least has a chance of knowing.
There wouldn't be a roll for that. I still remember where the offices were on campus. Again, the in-game back story would establish that. When the outcome is in doubt, a roll is needed to know something. When the outcome is in doubt, it's not up to the DM to force the check. The player of the PC has to decide to roll or just abandon the possible knowledge.
I don't understand on what basis you are saying that I, as a player, can simply decree what has happened to my PC in the past - a type of "god's eye view" authorship - yet you are adamant that the narration for ZoT can't unfold in the same way.
Because it's not the same. With Eloelle, she already has established that she knows the answer. She can't both know and not know the answer at the same time, nor can she simultaneously have backstory to demonstrate both situations.