All you have to do is turn people into a feature vector then KNN them. Perhaps once you're in a smaller neighborhood, you can do more intensive analysis for high probability equality matching.
That being said, if the database is small enough (e.g., in a limited scenario or by applying other non-vision filters first), then the state of the art methods do use a similar approach. However, in practice people use methods with much stronger priors than KNN. Because faces fall into a low-dimensional manifold[1], you can take advantage of that to constrain queries much more than with generic KNN.
[1] My PhD advisor has published several works about this topic, e.g., http://vision.ucsd.edu/kriegman-grp/papers/ijcv98.pdf http://virtualhost.cs.columbia.edu/~belhumeur/journal/invari... http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.123...