It seems to be a speed issue. If you notice, when you press Control in Illustrator, you'll see some text change in the status area ("Direct Selection" or something like that). So my guess is that Illustrator's message pump is flagging different states for things internally when Control (or possibly other modifier keys) are pressed and was only tested by human input, which ALWAYS has a delay between Control being pressed and C being pressed. That being said, the following works for me in Illustrator CS6 64-bit:acSendControlDown()
acDelay(50)
acSendKeys("c")
acDelay(50)
acSendControlUp()