The conditional logic has been removed and this field group is indeed on an ordinary “page” post type. The first screenshot in this reply was taken with all plugins (except ACF) deactivated on WordPress development version (3.9-beta1-27501).
The second screenshot in this reply is taken from a fresh install with WordPress version 3.8.1. Everything seems to be working. Sorry to bother!
Must be a beta bug? Oh well… so much for having fun in beta builds.
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