AppleID is a single sign-on used across a wide variety of systems (iTunes, iCloud, AppleCare, the Apple Online Store, the Mac App Store, developer.apple.com, bu

AppleID is a single sign-on used across a wide variety of systems (iTunes, iCloud, AppleCare, the Apple Online Store, the Mac App Store, developer.apple.com, bugreport.apple.com, Apple's CA services for code signing and push notification services, to name just the ones that come immediately to mind) developed by different groups, at different times, using different technologies, over a period of many years. Even ignoring hashes and authentication protocols entirely, the set of fully-functional AppleID passwords is still the intersection of the sets of valid passwords for all supported clients of all these systems. In other words, you're most likely looking at the feature of iForgot that prevents you from selecting a password that one of the other systems isn't prepared to handle, or at least might not have been prepared to handle reliably last time requirements were frozen for a major system-wide upgrade of the (internal) AppleID protocol.