Following experience comes from Nitish Nagpal:
Customer was able to add users in team foundation server level groups and collection level groups but not in project level groups. We checked all the permissions and later found out that he was using visual studio 2010 with TFS 2012. When checking the way changing permissions in TFS 2012 I realized that you can't do this with the VS 2010 IDE when connected to TFS 2012 because in TFS 2012 some administrator features were moved to web-based only. For reference: http://social.msdn.microsoft.com/Forums/vstudio/en-US/fa7ce28e-8d26-423a-a0cb-88c3b14d2775/tfs-2012-from-vs-2010-disabled-the-add-button-in-group-membership-window
So, the only way to change these permissions when you don't have VS 2012 is by using the TFS 2012 Web access. You could also download and install the free VS 2012 Team Explorer, which will open the web browser windows you need when setting these permissions. NOTE: TE 2012 itself is free, but you still need a CAL for each user connecting to TFS.