Oliver,
Apologies for the delayed response, but this is a known issue around how docker.inside is implemented. It was very painful when setting up the docker image.
When using the packaging image in Jenkins builds, we have to invoke Docker manually (or run with arguments) rather than using the inside command.
The sudo-able packaging test images use a different approach, by applying templating to Docker files and rebuilding so you can always have a correctly permissioned user.
After some tinkering, I hit upon a much better way to do this, by dynamically creating a user within the container on the fly (which is also granted sudo permissions within the container). There's a PR out for this:
https://github.com/jenkinsci/packaging/pull/54
It's still pending review from someone though, but it's been tested out and works (was actually used for something small). If it gets the community nod, we could merge and have a more robust system (the approach you use requires having a local user created).
Hope that helps clarify somewhat!
Sam