According to the Daily Mail, there have been reports of X-ray machines scrambling Kindle screens, despite Amazon's claims that it is impossible. Can X-ray machines have this effect?
Likely not (beyond the normal static shock associated with rubber conveyor belts).
I can bring two pieces of evidence I find convincing even though not as definitive as a full blown experiment:
This video which shows a Kindle safely going through an X-Ray machine at an airport without damage: https://www.youtube.com/watch?v=qBg_5G2YEDg
The expert opinion of Professor Daping Chu, Head of the Photonics & Sensors Group in the Electrical Engineering Division, Cambridge University Engineering Department.
“I don’t think the radiation used in an airport scanner would ever be strong enough to damage an electronic ink display,” said Professor Daping Chu, Chairman of the University of Cambridge centre for Advanced Photonics. "But you can get a build up of static inside these machines, caused by the rubber belt rubbing. If that charge were to pass through a Kindle, it’s conceivable that it could damage the screen.”