It makes sense. Without the password, you can't access your data.
For the example you posted, try contacting web site support to see what can be done to change your email registration.
You can also try contacting Apple ID Support to see if they can/will help.
Apple ID Support
Apple ID Support (2)
Apple Support by e-mail or chat Work through the screens to get a chat option.
Apple Support using Twitter
Or fill out and submit this form. The form is for iTunes, but it will get passed to the ID Support section.
From the article below.
Without proof of your identity via security questions and other carefully selected criteria, Apple Support can't help you reset a password or perform any other actions on your account. These policies are audited and reviewed on a regular basis.
Security and your Apple ID