Yeah, we were talking about that at one point. Though, as multiplayer has evolved/improved we could also now do some more direct PVP sort of modes, I think.
Not without it being possible to either be hit by something that would not have hit you locally or miss a player target that you would have hit locally
Actually, it would work just like enemy shots. So sometimes you might fire at me, and miss or hit me when it looks like actually the opposite should have happened (from your point of view). But from my point of view, I saw the shot and dodged it just like an enemy shot works now, no worries. And from your end, it will just look like a brief lag hiccup, or else like you just barely missed (because at the scale of pixels we're talking about, it's fairly ambiguous, anyhow, unless you're the one being shot at).
That's why I think this would actually work for some lighthearted PVP. But because of the nature of the way the game is constructed, it would never be good in terms of anti-cheating measures on its own (not like an RTS that is in sync), of course the really serious PVP wouldn't be advisable. Too many ways to hack the client. But if you take that part out of the equation, the rest should work well enough to be fun and playable in PVP, I think.