Since you ran a grounding conductor with the feed to the subpanel, you do
not need to install a ground rod at that location.


Simply not true. Anything beyond a single branch circuit to a remote building
requires a ground electrode system. The only thing a 3 wire vs 4 wire feeder
affects is regrounding the neutral at the remote building.
http://members.aol.com./gfretwell/su...g2subpanel.htm