Uhh..the circles are not from the UI. That's like saying my banner that I throw down to buff my team and myself is also "The UI". Which it most certainly is not.
The UI consists of your skill bar, health bubble, dodge meter, mini-map, chat log, menu on the top left and your quest log. At least that's how I look at it and from what I've seen that's how the majority of the people here look at it. Majority rules imo.
Everything else is not the UI, it's the game, the world, the environment and the task at hand.
They have to have some minor thing to aware the player of incoming damage or else everyone would be getting hit by AOE all the time. To create proper boss fights you need some kind of awareness, no matter how miniscule it is. You look for circles on the ground for incoming AOE, you listen to sounds from the enemy for incoming buffs/debuffs or attacks and you watch the enemy's movement's so you know when to dodge. That's where "play the game, not the UI" comes from.
You can be really anal and call it all the UI, but know that you're a minority in thinking this way and Anet does not think of it this way.