The emails from email@example.com that usually indicated successful calculations now always indicate 0 invoices were calculated. Yet, tax is still appropriately calculated on all invoices in Zuora.
This will happen when the tax codes in Zuora are using an external tax engine. You will want to go to Setting->Z Billing Settings->Setup Profiles, Notifications, Email Templates->Bill Run Completion|Completed Status->[Edit]
Disable the call out.
This will stop the emails from being sent.