For some reason I failed to determine, the syntax I posted earlier didn.t work.
However, using the below instead, did.
mysql_insert('_accesslist', array(
'userNum' => $user_num,
'tableName' => 'apply_for_cme',
'accessLevel' => '6',
'maxRecords' => '1000', // max listings allowed
'randomSaveId' => '123456789', /
));