The problem is that you're explicitly telling the script to pipe it's output to the garbage heap by using ">/dev/null". I realize that the wiki article you quoted uses this exact syntax, and most likely your cron job is actually running. It's just discarding the output as you requested of it. I had a little difficulty getting my jobs to run, and identified a few items that may be of use.
1) Sometimes my jobs would be terminated right after starting them in the SSH terminal window. Using the "nice" command made this stop
2) I needed to make sure the entire command was on one line. Turning off autowrap helped me here. Do this in the crontab editor by pressing "alt-W"
3) I made sure to pad my job runtimes to two digits, but this isn't relevent in your situation
4) I entered a blank line after the command, then saved.
Here's an example of my functioning script that dumps the output where I expect it to be. You can check the impact of running your script hourly by logging into "http://yourdomain.com/stats/resources". Keep in mind this has to be on one line in the crontab editor. It'll probably wrap here.
01 03 * * * nice -20 /usr/local/bin/perl /home/*username*/awstats/tools/awstats_buildstaticpages.pl -config=yourdomain.com -update -awstatsprog=/home/*username*/awstats/cgi-bin/awstats.pl -dir=/home/*username*/yourdomain.com/statistics/