This has happened again - this time another Google Nexus 7 user running our app in a restricted profile for one of their children.
The app works fine in all my tests on all devices (iOS and Android). It even works fine on my Google Nexus 7 when I set up a restricted profile. I have never been able to recreate this error on any device.
But - as per the rest of this thread, I have heard from several other customers who have experienced this issue in the past.
Even weirder, apparently after rebooting the device for a second time the app then worked. They'd already tried rebooting once and that hadn't helped.