true damage is always relevant, because any bit of armor will lower your dps elsewise.
the reason why aya is considered so op is because she has high damage, fast scaling, and high mobility. Being mobile means being able to gank more often, and avoid ganks.
Specifically, her rush is extremely long range (2100 at level 4, just level 2 is enough to escape from anything), her F adds a huge amount of damage (it's like +67 pure damage, against a hero that has maybe 7 armor, that's the equivalent of over 100 physical attack), and her R deals spell damage and scales very well with her agility. Her C means she can avoid being slowed while chasing someone, or can escape even if slowed. She carries as hard as she does because she has a lot of additional damage that ignores armor, and has enough mobility to get in out of any situation.
Aya is going to end up farming better than most other carries, as the benefits of a kill don't usually outweigh the detriment of dying, which she can avoid.
But really ero, if you want to discuss this, go on irc. I understand where you're coming from, but you're picturing these girls in some sort of 1v1 deathmatch, rather than the context of a longer game.
Edit: specifically, irc because it's easier to discuss these things on irc then on a forum
