Google discourages the practice of having personal information, like user emails, logged to Stackdriver, even though it is possible.
If the developer initiated the logging of personal data to Stackdriver, then Google could state that it's not their fault, so don't fine us. I don't blame them. That's what I'd do also.
What could be done, is to encrypt the email. But if the user doesn't want their email known, then encrypting it, ultimately won't comply with the users wishes.
Using the Active User Key assumes that the user is going make a note of their key, record it, and then contact you with the provided key. Good luck with that. But, that may be all that your left with unless you want to make it clear in your Terms of Service and Privacy Policy that in some cases the account email might be sent to you.
If there is an error, and email service is authorized, the code can send an email from the account to itself. That way the information isn't being transmitted outside of the account.
I am very much in favor of protecting user information.