I am a long time Debian user and a moderator of the http://ask.debian.net
When you install Debian, from scratch, as you call it (actually from a net-install) . . . you don't get "any desktop environment" or any Apps. pre-installed.
You select the D/E and W/M at the time of install, then have to install 'all' the Apps. yourself -- later.
If you go to the main Debian website to download the ISO files ... there are 10 or more DVDs;
Granted you only need the 1st DVD of the set, to install Debian, then must install the Apps via internet connection "or" download the entire set of DVDs, if needed.
I once bought a DVD of Debian 5.0 Lenny (3.7Gb) that had the ISO, a selection of D/E's and the basic Applications, on it.
If you decide to select to download a DebianLive CD (not an official version of Debian) ... you can select to download the Desktop Environment of your choosing.
The various derivatives of Debian (like LMDE or Crunchbang) make the Debian installation and set-up process so much easier.
To answer your original question ... the LinuxMint Devs took a straight Debian 'testing' and re-configured it for Mint.
The development of LMDE is in no way connected with Crunchbang.
On my main PC, I have 3 OS's . . . LMDE, #!Crunchbang-Statler and Debian 6.0 Squeeze.
Crunchbang-Statler r20101205 (based on Debian Squeeze) was just released a couple days ago.
Debian 6.0 Squeeze ... is in the final stages of 'freeze' to be released as final 'stable' before Christmas.