Maybe I’m just assuming that “centroid” always means “center of volume” when it doesn’t?
Well, it depends on what “center of volume” means. If it helps, recall that the centroid is an arithmetic mean, not a median. With my example, imagine that there is a uniform mass density, so the centroid is the balancing point. If the two balls are very nearly (but not exactly) the same volume/mass, and the distance between them is relatively great, then you wouldn’t expect to be able to balance them by putting your finger adjacent to (or within) the larger sphere.
