So I've discovered that my sound card has a "PCM Playback Volume" control, but changing that control does not alter the volume. This is not only confusing but also a problem for PulseAudio. (PA merges this control into it's overall volume, and so when the user moves PA's volume control, in some ranges nothing happens.)
Interestingly enough, this control does not come from the HDA parser, it is added by alsactl at boot time...! (Through alsa-lib's snd_ctl_elem_add_integer, which does an snd_ctl_ioctl.)
So the question is, why is alsactl creating volume controls, and why is userspace allowed to add controls in the first place, if the kernel can't use them for anything anyway? That doesn't make sense to me.
This a generic problem, but sound card info, if that matters, is available here: https://launchpad.net/bugs/625149 Codec: http://launchpadlibrarian.net/54478760/Card0.Codecs.codec.0.txt