Personally, I think even passive abilities has cooldowns, but when the passive effects is discrete, not continuous... Ever heard of an in-game ability that removes buffs every x seconds?
(The discrete is like Evasion, removing buffs, anti-spell, etc. The continuous is like auras...)
As for negating an ability, I think there's an in-game item that negates an ability casted on her, and wait for x second to be ready to negate next ability cast on her...
(Or, something like removing effects and buff on her each x second, just as above...)