What tool do you use for showing the Audio bitrate?
Try MediaInfo to make sure that Handbrake is the problem here.
But as far as I can see, you aren't doing anything wrong (besides setting the audio bitrate this low ;) ).
The avcodec AAC encoder also has quality settings, you can try these out as well, should give better compression efficiency. However, avcodec AAC is generally not a good AAC encoder, you'd have to compile Handbrake with FDK-AAC support for good AAC encoding quality in Handbrake.
The alternative would be to use Vorbis or Opus instead, which won't go into an MP4 container though, but provide higher compression efficiency, especially Opus is just superior to any AAC encoder.