Keep in mind that some Aura actually give the creature the ability. For example: Quicksilver Dagger reads
Enchanted creature has "

: This creature deals 1 damage to target player. You draw a card."
In this case, while you do still control the enchantment - the ability is granted to the creature. So if you put Quicksilver Dagger on an opponent's creature they still control the creature including all its activated abilites... so they can now activate the ping+draw ability and you cannot. A legal play, but a poor play.
Actually, in this example, wouldn't you be drawing the card instead of your opponent? I'm thinking you still control the Aura, so you refers to the owner, you.