After the combat phase, can hexes be claimed even if the ships weren't involved in combat?
You interpreted the rules correctly. The rules state:


  if your Ship is in a hex without an Influence Disc after the Combat
  Phase, you may place a disc there.


Which does not require that you actually participate in combat, just that you have a ship in a hex without any influence disks. So you are allowed to claim an influence disk free hex by ending your turn with a ship in that hex.

This forum post at Board Game Geek discusses the same question.