The other idea I can conceive is that somebody with a broken screen try to test the materials Young's module, yield/tensile strength, thermal expansion coefficient and especially the fracture toughness. Then one can measure the size of the screen. Then take a screen which is still working fine. One can use the optical/acoustical interferometer to measure what is the strain distribution within the whole screen, combine with the known shape of the screen and Young's module one can calculate what is the stress distribution within the whole material. The next step is to determine what is the maximun defects size in the material using ultrasound or X-ray scan. The material can break basically in two ways: either the stress in the material reaches the tensile strength or the combination of strain and defects exceed the fracture toughness. From the image here it looks very likely to be the latter case. Take a look here:
http://en.wikipedia.org/wiki/Fracture_mechanics
And it would also be a very good idea to take a look at the fracture cross section under the electron microscope. Here one can identify clearly what defects causes the fracture.
Indeed this is not a joke. They are completely doable and those people design the device should test that. I think the most probable cause is that there is some intrinsic defects in the screen in perhaps a few µm range, and during the mounting of the screen too much stress is accumulated somewhere so that the K
I value is very close to the fracture toughness. The material does not break at that time but a little increase in the stress, by either users touching or the temperature change, will cause catastrophic failure of the material.