Weird how people missed it
1. The device is running iOS 6 or earlier.
2. iOS lock delays double on each wrong entry, until reaching 30 minutes or something, before being completely disabled with a "Connect to iTunes" error. This error, therefore, is a result of a wrong time setting on the iPad (kids wind the clock ahead for cheating on games), then a wrong passcode attempts, then an auto-corrected time setting (possibly when the iPad auto-reconnected to Wi-Fi).