Owner col should be visible only if $perm_adit = "own", not ALL.

should be:

/* If user has all edit permissions show zone owners */
if ( $perm_edit == "own"){
echo "<th><a href=\"javascript:zone_sort_by('owner')\">" . _('Owner') . "</a></th>\n";
}


AND:

if ( $perm_edit == "own" ) {
echo "<td>" . $zone['owner'] . "</td>";
}