The subpanels ground is not bonded to main panels neutral busbar
Short answer, you do want a ground conductor between the main panel and subpanel (not just a ground rod at the subpanel) and you only want the neutral bonded to the ground at the main panel.

The ground rod alone is not sufficient - although there would be a path through ground back to the main building's ground, that is not a low impedance path, it wouldn't be low enough to clear a fault, not safe, etc.  

The ground conductor could be a metal conduit from panel to panel provided it's installed properly so that it creates a continuous path back to the main panel.