When downloading the "install from network" ISO image for Fedora 19, I hadn't realized that the systems with Secure Boot (UEFI) are 64 bit, and so downloaded the 32 bit installer. The installer ran fine, and everything seemed great, but when I rebooted after installation was started all I got was "No boot disk has been detected". So the 32 bit installer should try to detect a 64 bit system and/or UEFI system, and say "This looks like a 64 bit system, are you sure you want to install a 32 bit version of Linux?"
This bug appears to have been reported against 'rawhide' during the Fedora 20 development cycle. Changing version to '20'. More information and reason for this action is here: https://fedoraproject.org/wiki/BugZappers/HouseKeeping/Fedora20
Installing a 32-bit OS on a 64-bit system is a valid use case. If the system is able to boot from the 32-bit installation media, which does not include an EFI bootloader, then it's likely that the system will be able to boot in BIOS mode from the hard drive post-install. More importantly, there is no way for anaconda to know if the system would not be able to boot in such a case. This is a BIOS configuration issue.