Right there, you did it again. A stiffer ski with a slower rebound speed does all that - even though it might dissipate less energy per vibration cycle than the softer ski.
Damping only tells you how much energy is lost per vibration cycle.
Proving my point yet again. Notice that the ski designers I linked to above do
not call that characteristic "damping"
“Vibration damping” has become a popular, often misused, term in many industries including skiing. The most common mistake is ...
blog.sandwichtechskis.com
Notice:
and neither do careful ski reviewers. Blister, for example, refer to 'suspension' - with suspension speed, suspension travel and suspension damping being entirely separate quantities.