I'm surprised at the intensity of discussion here. I've only ever had one bad DM in the past and my question was not meant to suggest that I lack trust in my players. To suggest otherwise only tells me that you may have had negative experiences with your DM's in the past, because I know that my players trust me completely If I wanted to roll on their behalf for the immersion. If they were really concerned about it, I would gladly photograph the dice results and show them when things were resolved in game.
In regards to why I think secret roles are just as effective or more effective than denying a roll in the first place, I always believe in giving a player the right to try, or to try again and again at the cost of time and possibly resources (with time comes hunger and thirst).
One of you mentioned that you simply disallow follow up roles for say, searching for secret doors? Before, it was indicated that if the player stands around trying again and again to succeed, it wastes time... Well maybe, unless such a simple situation, searching for something with a certain uncertainty is entertaining! Ok, so your characters might waste time in their minds, but you the player might be desperately hoping against hope for a secret door. Not finding anything after putting in so much effort might also be as rewarding story wise as the DM revealing that "You hear a click, after several hours searching the wall slides open in front of you"
Just another clarification. I don't botch results to go against my players. In fact, I'd find the insinuation a little bit insulting if I didn't think that the person who said so might have had some bad experiences with a DM in the past.
In regards to not even getting players to make a roll in the first place, the nastiest thing I did to them was have them come up to the BEBG drow sorceress who was true polymorphed into a prisoner they rescued. They didn't suspect her for a moment, only looking at her with a gem of true seeing. With her 20 Charisma, actor feat and +9 deception and the fact that they had just ripped a face hugger aberration out of her throat and the fact that they never once questioned whether she was safe, they did the unthinkable, they saved her by volunteering the teleportation circle coordinates of the elves she wanted so badly to destroy. The players role played their devastation on returning to the smoking ruins of the elves. The players themselves loved it. They were truly deceived out of game and in game and were completely caught off guard.
In saying all this, if one of the players had not trusted the sorceress and started questioning her, I was going to let them fight and possibly kill her then and there. I have no qualms with players being on the ball and destroying my bad guy's plans because it makes for GREAT story.
I'll have to look into the passive perception skill some more too

. I like the idea of me keeping a tally on player hp, but not all the time, maybe when they're on another plane or something, where their senses are warped.