thats not quite right.
cc stops attack and spell cast windup animations, but not the cast or actual attack animation.
if you cc someone right as they are winding up an attack, it will stop the attack, but if they successfully launch the attack (projectile is in the air, or melee champion is in mid swing), then nothing except death will stop it, whether it be a knock up, flash or whatever. If you've ever shot someone with a ranged auto attack but died before it hit the target, and it did no damage, thats what that is. Its the same with melee champions dying mid swing.
Some spells have an instant windup animation but a long ass cast animation, like ezreal ult.
But spells and attacks can be interrupted, the window for doing so is on the windup and is really tiny, so people assume its not there.