How do I send an email to GAE on behalf of yahoo, hotmail or .edu?

In GAE, a non-gmail user can create a Google account using non-gmail email and log in to the Google app. However, sending from this email does not work all the time.

For example, suppose foobar@yahoo.com creates a google account and they sign up. The GAE should then be able to send email to foobar@yahoo.com during a user request.

The problem is that this does not work for Yahoo and others email accounts. In my experience, only the following users can be sent on their behalf:

• Currently logged in gmail users
• Currently logged in users with emails that run in Google apps
• Administrators

However, you cannot send email on behalf of users with the following email address:

• Yahoo and hotmail users
• .gov or .mil
• most .edu users, although I think some schools use Google apps and they work.

If I send from these email addresses, I get the following error:

   message.send();
  File "/base/python_runtime/python_lib/versions/1/google/appengine/api/mail.py", line 799, in send
    raise ERROR_MAP[e.application_error](e.error_detail)
InvalidSenderError: Unauthorized sender

Did I miss something?

I know that there are similar questions on this topic, but I do not think that they nail them.