Tested on a lsb images which enabled pam for crond.

Non-root user can't perform command 'crontab -l/-e'.

The error logs from /var/log/auth.log:
Jul 12 02:36:14 qemux86 unix_chkpwd[768]: could not obtain user info (test-pam)

root cause:
unix_chkpwd can't get user info from '/etc/shadow' because it has incorrect permission settings:

root@qemux86:~# ll /etc/shadow
-r-------- 1 root root 1090 Jul 14 05:29 /etc/shadow

On a ubuntu host it is:
-rw-r----- 1 root shadow 1389 2011-07-07 18:04 /etc/shadow