Hi John,
The reason that "Have their Center In" does not give you the SUM of the smaller polygons is because this match option matches the join features if a target feature's center falls within them. Basically put, if a larger polygon's centroid falls into a smaller polygon, that smaller polygon will be joined. Here is the text from the help:
"HAVE_THEIR_CENTER_IN�??The features in the join features will be matched if a target feature's center falls within them. The center of the feature is calculated as follows: for polygon and multipoint the geometry's centroid is used, and for line input the geometry's midpoint is used."
So if you have an instance where there is not a smaller polygon existing where the larger polygon's centroid is, you would actually not get a match. Hope this helps to clarify the behavior you are experiencing.
Matt