Ah, I just now saw that a post went up on Meta.SO shortly before I posted this question (I did look there first, but missed it.)
Apparently link shares directly to answers weren't being counted properly before, according to this bug on Meta.SE. This was apparently fixed today, so the proper counts are showing up now and the newly-awarded badges are correct.
The original queries the sharing badges, Announcer, Booster and Publicist, were supposed to count the total number of unique IP Addresses that visited from a link shared to a question.
In order to calculate this we would use the PostId from the link shared and join back to the Posts table to aggregate the total visits under each question. This process worked great for questions shared, but as you found out there was an issue when answers were shared. There was a bug that was introduced into the code during an earlier optimization that wasn't properly looking for the ParentId when an answer was shared. As a result, answers were not being included in the awarding of badges.