Just wanted to add to this thread. I found out that this might be related to using the iCloud Keychain on iOS and with a computer using Mac OS X. Due to how iCloud Keychain stores all passwords across all synced devices, which can be both iOS devices and Mac OS X computers, the methods for accessing and updating those passwords has changed. Not sure whether this is intentional by Apple or not, but it seems that the ability to update passwords stored in iCloud Keychain is not something you can do through iOS (or at least, I have not been able to find a way to access the keychain and view/update any of the passwords stored there).
If you have a computer set up to use iCloud Keychain, you can use the Keychain.app to view/modify any passwords that are stored there, which "should" update the passwords stored on the iOS device, if that keychain item is actually synced to the iCloud Keychain. (Tested this and confirmed)
The problem appears to arise specifically if you only have one iOS device (or only have iOS devices) using iCloud Keychain. The option to update passwords seems to be missing. Not sure it this is new to 8.3, but this is the first time I have run into this problem, and cannot seem to find any reports detailing this problem anywhere else. In fact, to a greater degree, most articles/sites that discuss the iCloud Keychain only refer to the usernames and passwords stored by Safari, which are not the only passwords and information stored by the iCloud Keychain. This issue being a prime example.
I did notice that when re-adding my gmail account using my iPhone, the login page was actually just a webkit presentation of the gmail login page (webkit being the underpinnings of Safari, used for displaying HTML, but not actually the full app or Safari), which is where I entered my username and password, which I am assuming is now stored in my iCloud Keychain. I even checked in Settings>Safari>Passwords&Autofill>Saved Passwords, and my gmail username and password are NOT listed there, so iCloud Keychain is storing some items somewhere else, which is not accessible by the end user through the UI.