Water doesn’t fall in inverted half cup

[Kashmir]

I just happen to see a show about air pressure host by Brian Cox. As the link:https://i.stack.imgur.com/vfZlI.jpg shows, he flipped a half-filled water cup upside down then the paper on cup doesn't drop:
It puzzled me, because the cup is half-filled, the pressure shouldn't balance since inside water pressure+atmosphere pressure should be bigger than outside atmosphere pressure only.

What’s the explanation?

 

[hutchphd]

What does the film say?
The paper deformation will allow a negative pressure to develop inside the glass. The 5 cm of water in the glass will produce a gauge pressure of ~.005atm (10 m is one atm) so the air volume will need to expand by .5% to create that suction. In addition both paper and glass are hydrophyllic and the surface tension at the boundary will tend to retain the paper in place. Apparently the combination is enough.
Can you devise an experiment to test this explanation? I can think of two different ones.