Lusche's animation is the best setup for this.
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This is two players BOTH filming a collision. The P47 is flying strait and level so BOTH films are layed over each other placing the P47 in the same spot. Watch as the pony closes in. From one players view the pony NEVER got any where near hitting the others, however the other player's computer detected a collision and so marked it as such.
If you were watching the pony closing in and before you thought he was even close your plane falls apart and falls from the sky. 
Personally I'd rather have my own fate in my own hands and work to AVOID hitting other planes instead of just having my plane fall out of the sky because some one flew by close.
Really good example of lag and how it pertains to online gaming.
Not to get too far off topic, but back in the mid 90's... I used to play Mechwarrior 2 Mercs online... over dialup. Understanding lag and how it works was critical. A tactic called "lag shooting" was developed back then. Once you figured out how much lag there was between your opponent and yourself... you would simply over compensate your lead on the target to shoot at where he "really" was (or was going)... not where he appeared to be.
At least AH has that built into the client side so where you see your target, is where you shoot, and if you hit him on your screen, he takes the damage.
Can you imagine the whines of people now if they had to learn to lag shoot... and do it for 10 - 20 different opponents in the sky at the same time... all with a different latency?
