Maybe a little late, but I'm offering a partial/experimental answer in the hope that other community members may provide concrete explanations. If you are willing to take the risk and experiment, perhaps it will work in your setup too.
I'm running Linux Mint 15 64-bit and had the same problem with my Canon MF4570dn. I installed version 2.70 of the 64-bit driver from Canon's website:
sudo dpkg -l | grep Canon
ii cndrvcups-common 2.70-1 amd64 Canon Printer Driver Common Modules Ver.2.70
ii cndrvcups-ufr2-us 2.70-1 amd64 Canon UFR2 Printer Driver for Linux
I had the exact same problem that the computer says “printing”, but nothing happens in the printer. After much frustration, I came across two sites that mentioned some 32-bit libraries are needed for the Canon drivers and suggest installing the following:
sudo apt-get install libc6-i386 ia32-libs lib32z1
I did this and my printer works. For reference, the sites are:
Note that the sites also mention some symlinking, but I did not need to do this (in fact, on Mint 15, the referenced folders did not exist on my machine).
I don't understand why I need to install 32-bit dependencies on a 64-bit driver package (it is not listed as a requirement in Canon's documentation), which is why I call this a partial/experimental answer.