After Ubuntu 10.04 LTS (Ubuntu 10.10 works, Ubuntu 11.04 doesn't work at all, Ubuntu 11.10 and newer have the bug), the headset only plays sound at maximum volume level if the volume is turned down just a little no sound is being played.
I have filled a Ubuntu bug for 12.04 LTS at: https://bugs.launchpad.net/ubuntu/+source/alsa-driver/+bug/1200925 . I was advised to contact this mailing list.
AlsaInfo for Ubuntu 12.04 LTS with the bug: http://www.alsa-project.org/db/?f=3bde76b15a15f585418a6a4a4703ca67fd4cdf42. AlsaInfo for Ubuntu 10.04 LTS without the bug: http://www.alsa-project.org/db/?f=5824e55345c3f7128937405254485a489886b9dc
It is strange that dB range of your usb audio is 0 to 0.14 (only small gain and no attenuation)
In 10.04 LTS pulseaudio provide software volume control
( 1.095| 0.000) I: alsa-sink.c: Driver does not support hardware volume control, falling back to software volume control.
control.6 { comment.access 'read write' comment.type INTEGER comment.count 1 comment.range '0 - 37' comment.dbmin 0 comment.dbmax 14 iface MIXER name 'Speaker Playback Volume' value 30 }
In 12.04 pulseaudio did not provide software volume attenuation and use the speaker playback volume control