I'm not sure that documentation is correct - there were some changes in the installer for F17 that lowered that memory requirement and we explicitly tested installs with 512 MiB (the hard coded minimum for install with Fedora 17). I've seen reports of successful installs with 384 MiB and enough swap (using the nomemcheck boot parameter) but AFAIK, that isn't supported and YMMV.
As far as why the installer needs that much memory, there are several things but yum, rpm and selinux are big memory users.
While it is a little old, one of the Anaconda (the name of the installer used in Fedora) developers did an analysis on where all the memory is used during installation [1] which I found to be rather interesting.
I believe yum, Fedora's package manager, is the one with the RAM requirement. Packages are represented in Python (the language in which yum is implemented) as objects, which take up a chunk of memory per instance.
As others said, it's because of the sucky Python install tools. Once installed you can get rid of that lot and it'll run in smaller amounts of memory, although still not nearly as small as one of the Linux distros that's designed to be minimal.
