Using opponent's first sequence spaces
That's right, you cannot use your opponent's sequence space.

But what it also mean is that a player/team can use a chip (of their own) already in play as part of a SEQUENCE, to complete another SEQUENCE. So if you e.g. have a horizontal SEQUENCE you can use any of these chips to complete e.g. a vertical SEQUENCE.

So no one can place a chip on top of another chip that has already been placed on the board.  


  Set-Up
  ... Once a marker chip has been played, it cannot be removed by an opponent except when using a one-eyed Jack as explained below...


And by the normal rules you cannot remove chips from a already completed SEQUENCE.  


  The Jacks
  ... You cannot remove a marker chip that is already part of a completed SEQUENCE. 
  Once a SEQUENCE is achieved by a player or a team, it cannot be broken...


SEQUENCE Rules