Let's say we've this scenario:

0.7s - Client sends data (still in fire)
0.71s - You move out of fire
0.99s - AE goes off on server
1.00s - Client sends data

Now, at 0.99s, what data does the server have? All it can see if you're in fire so you take the damage. The data that come 0.01s later is too late, and this is why you get hit by AE despite seemingly dodging it. Timestamp wouldn't matter, because the server already made its decision prior to the next client update. Now, you can have server wait up to an extra 0.3s to consult the client info, but that'd mean even more lag, and this game is laggy enough as is.