If I edit the print url to point to an arcgis server print service (not secured) everything works fine and I get the printout from that server. I if edit also the webmap id in order to point to a secured web map (shared only to organization) I am asked to login as expected and after the webmap shows up but if print I don't get a printout back. (I see that there is a request but no response). So despite the login the arcgis print service does not know how to access the secure webmap ?
We were able to do a workaround for our internal users (block at the firewall, leave unsecured so it can print). Otherwise I'm hoping this is a bug that is fixed in 10.2, though I haven't yet confirmed that.