Arbitrary said:
The rules as written. Ok.
Opposed Checks, page 178
Sometimes you make a skill check as a test of your skill in one area against another character's skill in the same area or in a different one. When you use Stealth, for example, you're testing your ability to hide against someone else's ability to spot hidden things (the Perception skill). These skill contests are called opposed checks. When you make an opposed check, both characters roll, and the higher check result wins.
Stealth, page 188
Opposed Check: Stealth vs. Perception (see the table for modifiers to your check). If there are multiple observers, your stealth check is opposed by each observer's Perception check.
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It's perfectly clear that each entity on the battlefield is to get a roll against the stealther.
It also says under Passive Checks (page 179):
"When you’re not actively using a skill, you’re assumed to be taking 10 for any opposed checks using that skill. Passive checks are most commonly used for Perception checks and Insight checks..."
So you are making an opposed check, but it assumes you're taking 10 for your roll (effectively setting a DC of skill+10) if you aren't actively looking. It also says taking 10 happens outside of an encounter, so there's some confusion there, but:
on Page 186, it says the DM usually uses the PCs passive perception check, an active check requires a standard action.
on Page 262, it says to use your passive perception check
and on Page 281, it says invisible creatures use their stealth vs your passive perception, and you can use a minor action to make an active perception check.
so, passive checks are clearly used in combat encounters.
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From this, I think that the term Opposed Roll/Opposed Check includes both parties rolling, or one party rolling and one party taking 10 or using a passive skill, or possibly both using passive skill checks. It's still "opposed" in that a failure for the active stealther means a success for the passive perceiver, not b/c it requires dice rolls from everyone.
You don't need a hundred roll-offs if a rogue hides behind a bush from a squadron of passing orcs.