FFXIV uses a different netcode structure than other MMOs. Basically what happens in other MMOs is your client can see whether you were in an AOE or not and tell immediately when you took damage. SE went with the server being in charge. So what you end up with is:
Boss starts AOE on server end
You see AOE on client end and start to move
AOE cast ends server side and damage is sent out
Now, whether the whole "you moved" part gets back to the server before the server ends the AOE and calculates damage depends on latency and packetloss. In one of the interviews that Yoshi did recently (available on Reinhart's translation thread), it was implied that playing with a "3 digit ping" wasn't good. This would mean you need to be under 100 ms to not see any sort of delay, with very little packet loss.
Most people in the US/EU aren't going to have that steadily, and if you get into the higher range for latency it's going to start being difficult, if not impossible for you to dodge. Changing their netcode would involve lots of time and money, and unless they lose a bunch of subs to that issue, I don't see it happening. Instead they like to blame player's networks it seems (again, implied from most recent interview). Part of that probably has to do with Japan having a much different (better) internet infrastructure as a country. I imagine that anyone getting over 100ms ping there is a rarity, here it's common.
All of that being said, with the 2.1 patch they did try and help it along by increasing the positional update interval to .1 seconds. I don't believe it's possible to get it any faster than that realistically. If you're still unable to dodge, then endgame may not be for you in FFXIV :/ Yoshi said in the interview that people who want to do the endgame stuff and hard content need to have excellent setups, which in this case also means internet connection and hops.