You misunderstand how docker works. 'ubuntu:12.04' refers to a very particular image on the docker registry (https://index.docker.io/_/ubuntu/). That image is in fact identical byte for byte on all servers which download it. So any application built from it will, in fact, yield reproducible results on all cloud providers.
That way, a particular build of a platform (ubuntu-12.04-20130808) that we create on a cloud provider could be used, or alternatively a particular cloud provider's stock image (someprovider-ubuntu-12.04-xyz) or existing bare metal machine matching the general OS class in a conventional hosting environment could also be used.
The idea is that where bugs are found (defined as "application installs fine on our images, but not on <some other existing platform instead>") new tests can be added to the platform integrity test suite to detect such issues, and/or workarounds can be added to facilitate their support.
That way, when an application developer says "app-3.1 targets ubuntu" we can potentially test against many different Ubuntu official release versions on many different images on many different cloud providers or physical hosts. (Possibly determining that it only works on ubuntu above a certain version number.) Similarly, the app could target a particular version of ubuntu, or a particular range of build numbers of a particular version of ubuntu.
It's sort of a mid-way point offering a compromise of flexibility versus pain between the chef/puppet approach (which I intensely disagree with for deployment purposes in this era of virt) and the docker approach (which makes sense but could be viewed as a bit restrictive when attempting to target arbitrary platforms or use random existing or bare metal infrastructure).
Also, would you consider the architectural concern I outlined valid? I mean, in the case you are pulling down network-provided packages or doing other arbitrary network things when installing... it seems to be like there is a serious risk of configuration drift or outright failure.