Backports version contains more fixes than just the one listed in the bug above. If you just use the Precise ordinary version (with the fix above), you get the following error
403 Forbidden file type or location
Because the first thing Centos does is check for local mirror locations with this
And something in that URL is not liked by apt-cacher-ng.
The Precise backports version fixes this issue.
You can verify you have (or have fixed) the issue from your Ubuntu machine with these steps.
1) Firstly, set wget to use your apt-cacher-ng proxy
# wget run control file for current user
# tell wget to use a proxy, apt-cacher-ng which listens on 3142
2) Now ask wget to retrieve the mirror file. Note the extra \'s to escape the '&' to get the full url to wget
wget --output-document=- http://mirrorlist.centos.org/?release=6\&arch=x86_64\&repo=os
3) This will answer back with either 403 error as above (problem not yet fixed), or a correct list of mirrors...