Am I misreading it?
"If the characters are searching for traps, the character in the lead spots the trap automatically if his or her passive Wisdom (perception) score is twelve or higher. Otherwise, the character must succeed a DC 12 Wisdom (Perception) check to notice the trap."
This says to me that if the party is not searching for traps (i.e. has not told the DM that they are doing this), the character in the lead does not get a chance at an auto-spot.
At that point, the character in the lead gets to roll.
Here's the thing I'm seeing with this... it's the idea that the guy in the lead doesn't get to roll for the trap at all... unless he's stated he's searching for traps. So that second sentence "Otherwise, the character must succeed a DC 12 Wisdom (Perception) check to notice the trap." only comes into play as the second half of the previous sentence.
So if no one is searching for traps... no one will notice it passively *and* no one will get to roll to spot it. They will automatically run into it.
However... if someone is searching for traps, they start by 'Taking 10' per se. If that's enough, (passive Wisdom / Perception 12 or higher) the PC spots the trap automatically without rolling. However, if the passive perception doesn't auto-find it... the player gets to roll an active Wisdom (Perception) check in the hopes of rolling higher than a 10 (and thus higher than his passive number) to find it.
Basically, what it come down to is anyone who is searching for traps can roll to find it, and any roll lower than 10 is considered a 10 for the check (IE the passive Perception number.) Anyone not searching for traps has no chance of noticing the trap at all.