Where is documented that no other transaction can update a locked row?
You say:


  if there is any LOCK on a row, [then] no transaction (even without LOCK) can update the row


On the page you have linked to you can read that


  An exclusive (X) lock permits the transaction that holds the lock to update or delete a row


which means that before a transaction can update a row it must acquire an X lock on it, which is impossible1 if there is already an S or X lock on that row placed by a locking read in another transaction.



1 -- because X, which as we know stands for "exclusive",  is incompatible with any other lock.