That wasn't what I was suggesting - but if the shooter has a ping of 1000ms you can expect (1) the target's position to be inaccurate because it's late being delivered to the shooter and (2) client prediction placing the target and potentially correcting that placement once an updated position has been received. Hence the mention of warping - you don't need things happening in the wrong order for that to occur. Do you?

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Mm, I think I see what angle you're coming from now. It all hinges on your view that "you can expect the target's position to be inaccurate", which gets a bit more into the theory side of things. Wall o' text incoming...
Events out of sequence are required for warping, because warping is an error correction. Simple latency will not result in warping of anything but the player's own character because, for every other entity in the world, there's no error to correct. Because humans are inherently unpredictable (in a simulation sense, anyway), clients typically perform little to no prediction on other-player entities, going strictly by the data the server is sending, and thus, the client's view of them is already inherently accurate at all times. Or perhaps a better way of putting it is that
everyone's view of
everything is inaccurate. Nobody in a FPS game since Doom is actually seeing exactly the same thing as any other player in the game at any one time. Everyone is offset by their own delay resulting in their own sequence of events.
Say two players are approaching each other from opposite sides of a hallway at the same (actual) time, when you pause everything to look at it. Player A will see himself as already being, say, 4 meters down the hall before Player B comes in the far door. Player B sees the exact opposite - he's 4 meters into the hall and Player A just came in the door. The server sees an entirely different third sequence: both players have moved down their ends of the hall by 2 meters, simultaneously. All of these viewpoints are perfectly accurate to the data they're getting, but they're all completely inaccurate if you stop and compare them to any of the other POVs. It's all about the frame of reference.
The job of the networking model is to negotiate these differing realities into a common outcome. The method we currently have strictly defines the server's outcome as the only valid one, which is a simple and reliable way of doing it, but it winds up making every event involving a player look inaccurate from their own point of view.
Going back to our simultaneous hallway fight, let's say each player crouches down after they go through the door, and is hovering over their trigger aimed at the far door, just waiting for a headshot. Player A sees Player B stepping into the door and instantly fires. Player B does the same thing on his side. The server sees both of them firing over the top of a crouching target into empty doorways, and so it counts both their shots as misses. Player A and Player B each see the other guy get blasted in the face, then crouching down, and then firing over at the long-since-vacated doorway. They're both completely unharmed.
The server's view of events is the only one whose outcome matches the sequence of events. Its view is right, but only because we've initially declared and -required- it to be right. From the view of either of the players, the outcome is completely wrong.
A latency-compensated version of the hallway scenario would, for the server, show both players getting 2 meters into the hallway before dropping dead from clear misses. For each player, they'd see their enemy walk into the door, get blasted in the face, crouch down, fire, and die from a headshot, taking the player with them as they fall.
Each sequence of events here is now wrong from all POVs. It looks pretty darn weird to the server, especially if the players are shooting, say, giant laser beams to illustrate exactly where they were aiming (which, to the server, is at an empty door). But the server's not playing the game, so why should we care about what it sees? From the POV of each player, the compensated sequence results in an outcome that's a lot closer to what they saw than having their obviously perfect headshot do nothing at all. That would be a huge hit detection bug, right?
Latency compensation is, fundamentally, about deciding that some events should have a closer correlation between feedback and outcome than other events do.