You can see various way to debug this in "Debugging git repo permissions on samba share":
- setting different permissions for share
- mounting manually
- downgrading samba and git to earlier versions
- sudo - this works but I wouldn't want to use it unless absolutely necessary
- changing owner and group after using sudo
Andrew Myers suggests making sure your bare repo has core.sharedRepository set to group.
If not, set it and run
cd /path/to/repo.git
chgrp -R groupname .
chmod -R g+rwX .
find . -type d -exec chmod g+s '{}' +
If nothing works, make sure it isn't an issue related to the kernel version:
I've downgraded kernel to 3.11.6 and git add/commit as user started working again.
Update: The OP kamaradclimber reports (or tried to) that is was a kernel issue (bug 66251):
Git doesn't work correctly on samba share after upgrading kernel from 3.11.6 to 3.12.1
Fixed by this patch.