This is unacceptable - if an authenticated login is good enough to change account details and sign-in info, why isn't it good enough to close an account?
I'm not an Udacity customer, and after reading your account I never will be - I loathe these scummy tactics.
Many people (me included) hold the opinion that you should be able to control your data, which includes the right to ask a company storing data about you to delete it unless they have a valid justification not to (e.g. they may have to keep payment history for 10 years for compliance reasons).
In fact, in Europe it's so many people that that's the law.
I'm not an Udacity customer, and after reading your account I never will be - I loathe these scummy tactics.