The GitHub docs don't make it completely clear that AddEmails is also
switching to the new v3 response format, but new integration tests
verify that it is.
This is a breaking change, but it appears that this method has been
broken for some time now and no one has complained yet, so I'm going to
assume no one is using it yet.
Notably, this is also the first (of many, I'm sure) bug I've discovered
while working on the new integration tests (#98). Yay for better tests!