Fresnel said:

However, it's made apparent that while they 'know' what happens in the Hollow Mountain, they don't know the specifics of it, just that it is a place where failures and the weak are taken to die, useful to some greater purpose.

It doesn't actually say whether anyone knows this when they're just a student though. Or that it's used on the students as some form of motivational threat. The character in The Outcast Dead has been an Astropath for a long time, and is quite the powerful and respected one. They are the exception, not the rule.

And while it is an apt comparison… I ALWAYS hate seeing people compare what the Imperium does to the holocaust. Considering that every untrained psyker is at risk of causing as much damage as a nuclear detonation (trained ones only marginally less so).

There's no reason to believe that you couldn't have a somewhat irreverent group of Astropaths that trade taunts in their off time. Throwing barbs about how the other(s) really should have been sent to the Hollow Mountain.  This is the kind of thing a servant might pick up on.

 I agree. Even if you don't know the specifics of what the Imperium does to psykers, I think it could be pretty common knowledge that people who manifest pskyer powers are taken away. It would be difficult to obtain the forbidden lore that would let you know what actually happens, but their imagination can fill in the gaps.

Furthermore it's not just the official branches of government they have to worry about, but I think throughout the imperium people are somewhat distrusting of psykers in general. especially non-sactioned ones. I think many pskyers that somehow learned to manage their powers without being caught will have learned that it's often best kept a secret.

 If I recall correctly "The Outcast Dead" does describe the slow burning away of the victim's soul. It was known that this was a fate vastly worse than death. Although the astronomicon ensures the survival of humanity, the scale of operation, coupled with the physical and spiritual torture dwarves any real world event.

What a priviledged few in the high echelons of the Adeptus Astra Telepathica know, and what every choir Astropath and rogue psyker know are two vastly different things.

Everyone knows that the Imperium has a dim view of psykers. There are Witchhunters by the score, not to mention the Inquisition, the Black Ships, and the general hostility of the populace. But that they send them to a big mountain where they scream away their soul to power the mighty beacon of the Astronomicon, is rather a bit less common knowledge.

 The character in question was a good astropath, but he wasn't part of the leadership. He was a ship's astropath. From the circumstances of his survival you can infer that he didn't even lead a choir.

The character in question was an excellent Astropath. And you're forgetting that he knew absolutely nothing of the specifics until he was told them by the Astropath assisting his recover, who was very much a senior one.

And he was only being told to specifically encourage his case. It is a mistake to infer that such information is used as a goad on everyone who is training to be an Astropath.

***************************Spoiler outcast dead****************************

I want to add that thhe storie is taking place on earth, Holy Terra, near the palace and Storm Legion  characters appear…

They are in the best place in the all Imperium to deal with such facts, and all psycker characters presented there are very potent, powerfull and their skill praised by their pears. Even the burn astropath was one if not the best of the students from the best astropath, himself… You know the story.