To reproduce:

1) download and open project
2) enable VoiceOver on device
3) build and run for iOS
4) notice the behaviour is off (most cases can be seen in the video that the user attached)

WORKAROUND:

As of Unity 4.5 the issue can be fixed by adding the following:

self.isAccessibilityElement = TRUE;
self.accessibilityTraits = UIAccessibilityTraitAllowsDirectInteraction;

to Classes/UI/UnityView.mm in UnityView initWithFrame function. The fix for 4.3 is similar.