I currently have no access to TI cards, so I don't know exact wording. If it says "after Invasion Combat" it is clear that Invasion Combat has to occur.
If you'd have to defeat a Ground Force or Mech, the player holding the Crown could intentionally move his forces off a planet in order to hold on to the card.
On contrary to your reasoning I believe that making "Ground Forces dance around galaxy" in order to prevent any other player from taking the Crown would consume many resources, CCs and time.
And I've got the feeling this was already thoroughly discussed in some other thread, so better dig and find conclusions reached there than take the discussion one more time