I believe the answer here is that UIActionSheet is not intended to be used this way, and as a result may have side effects like these. From the Apple ActionSheet documentation, "UIActionSheet is not designed to be subclassed, nor should you add views to its hierarchy."
While this didn't cause problems for me in iOS 6, something has clearly changed in iOS 7 and I am more in favor of going down another route than trying to do something that contradicts the docs. Note that a workaround may be to pass @"" for the cancelButtonTitle rather than nil, but this causes other UI problems and may not be approved by Apple.
Alternative solutions:
- Create your own view and present it modally - I made a simple example project showing one way to do this.
- https://github.com/gpambrozio/BlockAlertsAnd-ActionSheets (no update for iOS 7 yet)