For iOS 7.0, I’ve found that the contentInset trick no longer works. This is the code I used to get rid of the margin/padding in iOS 7.
This brings the left edge of the text to the left edge of the container:
textView.textContainer.lineFragmentPadding = 0
This causes the top of the text to align with the top of the container:
textView.textContainerInset = .zero
Both lines are needed to completely remove the margin/padding.