I agree here: Let the Dice Roll Where they May. Though I hold this to the players too...a couple bad rolls and your character dies. If I want or don't want something to happen...it just does or does not, no roll needed.The DM can do whatever he wants, as long as its in good faith.
There's only 1 thing that is a big no for me: Fudging. You do it, you a bad DM. Respect the dice, if you dont want a probability of success, don't ask for a roll.
I get lost in all the Forgey Jargon...
But I HATE monster knowledge checks, and don't use them in my game. But, sure, I always let players waste their time making them. No monster in D&D has some special "win button", so the players knowing the monster is immune to fire is very much pointless as the monster kills the characters. And does the monster have a template, magic item, spell, special ability that your "know everything" roll does not know....well, too bad for you.