The figure in that paper incorrectly suggests that the method used was an average of the correlations, which can be accomplished in the way you suggest, but buried in the text is a description that matches 3dTcorrMap -Zmean, which doesn't reduce to the easier case:
Quote
Weighted global brain connectivity (wGBC) analysis
See the middle left portion of Fig. 2 for an outline of wGBC analysis. We developed the wGBC analysis method initially using MATLAB (The MathWorks, Natick, MA), switching to a more efficient function (AFNI's 3dTcorrMap) for the findings reported here. wGBC analysis involves seed-based correlation of each gray matter voxel with all other gray matter voxels. These values are then averaged together and the resulting value (i.e., that voxel's wGBC) is assigned to that voxel in a new brain map. Fisher's z transformation is applied to each (Pearson's r) correlation prior to averaging, and then converted back to r-values afterward. This process repeats for all gray matter voxels, resulting in a single brain map per subject reflecting wGBC.
(emphasis mine)