Moderately paranoid? Players, in my experience, aren't moderately paranoid. They should be put in straight jackets and locked in padded cells.
Examples I've had to deal with:
1. DM (Me): You come to a 20'x20' room. There's a door at the other end.
[prerequsite blank stare at character sheets for 30 second]
DM: Come on, guys, what are you doing?
Player1: How high is the cieling and what sort of stone is the room made out of?
DM: Uh... it's sandstone. The cieling's 10' high. It's a sort of mottled brown.
Player1: How mottled?
DM: Ordinarily mottled.
Player1: I don't like the sound of that, guys, it's too normal.
[Rogue checks the walls, floor and cieling for traps; Mage casts Detect Magic; Paladin Detects Evil. Nothing is detected.]
Player2: I don't trust this. What does the door look like...
[10 minutes later]
Player 1: Ok, I guess I step into the room. I've got the rope tied around me and the fighter's holding the other end to pull me back just in case...
Or my other favourite
2. DM: A barmaid walks up to your table...
Player1: I Detect Magic on her.
Player2: I Detect Evil.
Player3: I Detect Lies.
Player4: I Sense Motive on anything she says.
DM: Uh... she just wants to know what you want to drink.
Player1: We order a round of ale, and I Detect Poison on it when it arrives.
Now, these were two separate groups and, as far as I am concerned, ANYTHING that can be done to discourage this type of boring gameplay should be applied. Before anyone asks, no the party had never been poisoned by any barmaid before and no, they'd never wandered into an empty room that was trapped.
Oh, yet another example. I once had a room where they had to cross a bridge over lava. pretty standard stuff. Would they use the bridge? Nooooo, that might be too easy or exciting or something. Generally something OTHER than boring. So they teleported 20ft. over the flow. That debacle stopped play for a half hour even after I told them that the bridge wouldn't collapse underneath them.
None of them wants to take the slightest ammount of risk. Now, I agree that nobody wants a guy in the party that plays a CN half-orc barbarian that does a stripsease on top of the altar of the Dark One. On the other hand, alot of players need to harden up and take a chance.