After much deliberation and play testing, we have come up with another theory.
The card reads: "When drawing a dragon card, you may swap it with one already in your display."
Does this mean you can swap it with another dragon card in your display (previously drawn during this same delve) to fit your companion needs? Or is it any card on your display? (Like using a pilfer card over and over instead of having to face the dragon).
You can swap a newly drawn Dragon card with another Dragon card in your display, not a Pilfer card or a card with a chest.
The Knight is better at fighting dragons, so you have a lot more control over what type of dragon you face when you find one (any of the three cards in your display).
Hope that helps!