I generally agree with what you say. It is definitely a challenge to your authority. You can respond with the card and retain your authority, but I think you can also retain your authority by putting them in their place. If you call them out on their power challenge and challenge them to repeat it, and then they don't, you have essentially exerted your dominance.
Think about it from the team captain point of view. I knew people who would directly challenge the captain. "Why would I listen to you? Just because you wear a colorful band and you lick the coaches balls?" You have the captains that go, "listen to me because I am the captain" (Using cards) and the captains that just naturally lead their teams and don't really need to band to do it. (Using personality). Both are effective.