It works fine for me on Fedora 201, maybe you have a bug, or as mpromonet suggested, the archive is read-only:
[root@f20 ~]# tar czf /tmp/ul137194.tar.gz -C / /etc/passwd /etc/group /etc/shells
tar: Removing leading `/' from member names
[root@f20 ~]# mkdir /tmp/ul137194
[root@f20 ~]# archivemount /tmp/ul137194.tar.gz /tmp/ul137194
[root@f20 ~]# find /tmp/ul137194
/tmp/ul137194
/tmp/ul137194/etc
/tmp/ul137194/etc/passwd
/tmp/ul137194/etc/group
/tmp/ul137194/etc/shells
[root@f20 ~]# rm /tmp/ul137194/etc/shells
rm: remove regular file ‘/tmp/ul137194/etc/shells’? y
[root@f20 ~]# echo nogroups > /tmp/ul137194/etc/group
[root@f20 ~]# umount /tmp/ul137194
[root@f20 ~]# tar xzf /tmp/ul137194.tar.gz -C /tmp/ul137194
[root@f20 ~]# find /tmp/ul137194
/tmp/ul137194
/tmp/ul137194/etc
/tmp/ul137194/etc/group
/tmp/ul137194/etc/passwd
[root@f20 ~]# cat /tmp/ul137194/etc/group
nogroups
1archivemount-0.8.1-2.fc20.x86_64, libarchive-3.1.2-7.fc20.x86_64, fuse-2.9.3-2.fc20.x86_64