The touch screen works due to capacitive touches which are small electrical charges, so it might be possible for static charges to cause screen actions. So don’t rub your cat on the screen!
The Oasis should be grounded inside the case to prevent that though, but that doesn’t mean it didn’t get damaged in shipment. I know that when you mess with the internal chassis of electronic devices you should always wear a static discharge bracelet/device so that you don’t zap any of the electronics. But like I said above, the outer case should be grounded to prevent normal static discharges, whether that ground has been damaged is another question.