Getting root's crontab to run with root's privs

Question

I am trying to schedule a cron job to run some serveradmin scripts. If I edit /etc/crontab, the script runs as scheduled, but while it appears to run as user root, it doesn't appear to run with root's privileges.
Here is /etc/crontab and a simplified script:
headquarters:~ admin$ cat /etc/crontab
# The periodic and atrun jobs have moved to launchd jobs
# See /System/Library/LaunchDaemons
# mi hr md mo wd who command
0-59/15 * * * * root /Users/admin/log_afs >> /Users/admin/afs.log
headquarters:~ admin$ cat log_afs
echo ----
echo 'Timestamp: ' `date`
CONNS=`serveradmin command afp:command = getConnectedUsers | grep ipAddress | wc -l`
echo 'Number of Connections: ' $CONNS
Once I install this crontab, I get an afs.log created in the correct location with a hh:15 timestamp, owned by root. To me, this should mean two things
a) The job is running as scheduled
b) The job ran as root
Yet I'm getting output identical to that I would get if I'd run the script as admin (without the sudo prefix). Below is an interactive session:
headquarters:~ admin$ ./log_afs
Timestamp: Wed Nov 14 19:33:05 MST 2007
serveradmin must be run as root
Number of Connections: 0
headquarters:~ admin$ sudo ./log_afs
Timestamp: Wed Nov 14 19:33:29 MST 2007
Number of Connections: 10
headquarters:~ admin$
And below is the output from the cron job:
headquarters:~ admin$ ls -al afs.log
-rw-r--r-- 1 root staff 287 Nov 14 19:30 afs.log
headquarters:~ admin$ cat afs.log
Timestamp: Wed Nov 14 19:30:00 MST 2007
Number of Connections: 0
The script I want to run does a lot more than just count connections; I've simplified it here for discussion. My main question now is "How do I schedule jobs that require root access?" ... not "How do I report X about afs?"

Answer 1

I don't understand ... if the script is running as root (as evidenced by root owning the output file, and /etc/crontab sets root as the scripts owner) ... then why doesn't root have privs? Essentially, this is my original question.
Besides, my original solution was sudo crontab -u root -e with the same results. Editing /etc/crontab and setting the user to root was an alternate approach.
headquarters:~ admin$ sudo crontab -u root -l
Password:
# mi hr md mo wd command
0-59/15 * * * * /Users/admin/log_afs >> /Users/admin/afs.log
headquarters:~ admin$ cat afs.log
Timestamp: Thu Nov 15 08:45:00 MST 2007
Number of Connections: 0
headquarters:~ admin$ sudo ./log_afs
Timestamp: Thu Nov 15 08:48:40 MST 2007
Number of Connections: 10