My 18-month old will push the button just because he's experimenting with the device - this means instant dissatisfaction for his big brother, watching the movie (or playing an app) with him.
I think there is validity to the idea that you should be able to turn the touch interface off completely. Many apps exist where interaction is not only not necessary (movies), but often-times potentially very destructive to the use case (GPS/navigation).
Its true, though, that its up to the app developers, and having UI-navigation controls be 'staged' with phases and states is probably the best all-round solution. Still, I think it would've been nice to Apple to consider the case where you really, really don't want the app - or movie - to be interruptible.
You could always try turning the iPad upside down, he is probably less likely to touch the top of the device.