If you add a secondary contact, that you then give permission to be able to access Invoices (and/or perhaps other permissions), invoice creation notification emails only get sent to that person, instead of both primary contact and the secondary contact you also gave permissions to billing for.
Yes, this is a bug.
NO, do not try and say that "you gave this person permission to view and work with a certain part of your account, that OBVIOUSLY MEANS you dont need access or email alerts anymore!"
No dream-land logic or round-about excuses please.