Frankly, I agree with Mailchimp. Giving access to that information raises privacy issues (someone could potentially see that I'm subscribed to an embarrassing newsletter our at least use that information in phishing or advertising). Additionally it's a product that doesn't provide much benefit to Mailchimp and their paying customers

I suspect they meant that you'd use a check to make sure that you are in receipt of email to the address you want to check; similar to reset your password email, click the link in the email to prove it's your own email address.

How is showing me the lists I'm on a privacy issue?

Doctorow was on over 3,000 lists. Unsubscribing was a lot of work. The cynic in me says that's how MailChimp wants it.

Might be hard technically as well. I suspect it isn't one huge database with a nice indexed query to return all lists associated with an email.

Even then this should be possible to gather quite quickly and if not they'd still be able to collect it in a batch job and send result later by mail.

Assuming a database or table per list owner, that's X separate queries where X is the total number of MailChimp customers. Don't see how that would be quick or easy. MailChimp says they have over a million customers.