Unistalling the game and reinstalling it doesn’t effect your account. That the game installs a file onto your device, so there system can reconize your account. If that is the case, its a simple device wipe. But it still doesn’t make as much sense as to just tie your apple/android information to their database. If you have nothing to loose, try it and let us know.
Try wiping the phone by resetting it to factory settings through iTunes and re-installing the game. It still kept my account info. Data might have been retained because It will restored your data (it was restored to a point before you started playing the game). So it may have restored certain phone identification data that allowed it to recognize the account