I've never had a park ranger ask me for identification, and I think there is a reason. I've been asked for my wilderness permit many times, and I always have it. As a general rule, if some NPS ranger approaches a backpacker and asks to see the permit, it is just a routine thing that they do, especially on trails that are overused, and some people try to sneak around the quotas.
In the ten seconds before the ranger reaches you, he is starting to decide whether or not you are a possible violator. For example, if he smells dope and sees a big bale hanging off your backpack, he will have his mind made up in an instant. If he sees your tent pitched in an area where there is no camping allowed, he will have his mind made up. In those cases, he will often ask to see your identification first, and he can hold that while he asks questions about a possible violation.
But, if you are just on the trail, minding your own business, and the ranger walks up, often he will check the permit and you'll be on your way 20 seconds later.
A friend of mine used to be a ranger-naturalist in Yosemite, and he had some obvious violators on his hands, but he neglected to get the identification first. When he confronted the violators with the regulations that had been violated, they started to rough him up and refused to furnish any identification, so he left and got his buddies, the armed protection rangers. The violators were hauled in and spent the night in the slammer before a federal hearing the next morning.