Decision 23/2 says that
"If a stone is partially embedded and may be picked up with ease, it is a loose impediment."
Presumably, if Cink's ball were not in the way, the stones in question could have been picked up with ease. But because he would have moved his ball by picking them up, he was unable to, and instead removed them by gouging them out of the sand.
I am beginning to see the light here. It's just like Slugger White said - he was removing loose impediments. The rules do not say that you have to daintily pick them up between your fingers.