If you are running the default sendmail, put an alias for root in /etc/aliases and restart sendmail or run 'newaliases'.
Or you can edit
/etc/share/logwatch/scripts/logwatch.pl
and change line 64
$Config{'mailto'} = "root";
Exactly what I did earlier.
I would strongly recommend using /etc/aliases and NOT editing logwatch.pl as any updates to logwatch will collide with your edit, leaving you with .rpmnew files to merge.