Create a pod w/ an init container and a primary container. Mark the primary container privileged. Do not mark the init container privileged. The init container will run as root(or perhaps the image's default user). Now create a second pod, identical to the first but do NOT make the primary container privileged. The init container will run as an assigned uid (e.g. 1000600). I would expect in both cases for the init container to run as an assigned uid. (Note that the openshift build git-clone init container is currently only working *because* of this bug. git cloning fails when the git-clone container gets run as a random uid. I have a fix for that, it will need to go in before/when any fix for this bug goes in, though).
Jordan explained this behavior to me. Basically because the pod has to use the privileged SCC, the init containers end up running as their default user. When the pod doesn't have to use the privileged SCC, the init containers get assigned uids. I still find it somewhat surprising behavior that changing settings in one container effectively changes the behavior/configuration of another container, but it sounds like it's working as designed.