From the reference for UIActionSheet:
UIActionSheet is not designed to be subclassed, nor should you add views to its hierarchy. If you need to present a sheet with more customization than provided by the UIActionSheet API, you can create your own and present it modally with presentViewController:animated:completion:.
My guess is your seeing exactly why.
The reference for UIAlertController doesn’t have a similar disclaimer, but looking at its interface, my guess is Apple will add it before release.
My recommendation would be to just create a small view containing your picker and buttons and show and hide it as needed. It’s not that hard to do and your not pushing interfaces beyond their intended uses.