Further investigation reveals that this was caused because the mailing list the user was signing up to was NOT set in CC to be on the “Join My Mailing List” screen (a screen we never use). Because it was not checked to be on this list, CC assumed it was not to be revealed, and displayed “No Interests” rather than the name of the mailing list that the user signed up for. Simply checking the box to display the mailing list on the Join screen allowed it to be listed on the CC-generated “Change of Interests” email, problem solved.
Word to the wise: when using this plugin, make sure the list is enabled on Join My Mailing List even if you don’t use that screen!