For anyone following along, I think I found the problem.
-- The problem, restated --
After issuing a successful members/add call, the response to the subsequent members/results call contained an empty list instead of the list of newly added members as expected.
-- Suspected cause --
I was adding new members to a group, but these members were already GroupMe users (they belonged to other groups, etc.). They were new "members", but not new "users" and I think that's why they don't appear in members/results response. Perhaps that is what is meant by these words from the API docs:
"Failed memberships and invites are omitted."
When the new members are also new users, they appear in the response.
-- In conclusion --
I guess it is important to distinguish between "new user" and "new member". New users are those who have never registered with GroupMe; new members are existing GroupMe users who have been invited to join a group. New users can be created as a by-product of inviting them to a group using the API. In this scenario, the members/results response will contain the newly created user-members, otherwise the list will be blank.
Thanks for everyone's help!