Thanks to your suggestion I'm getting a bit farther. It turns out that there is a 'cd' missing in the build script. Unfortunately it is in a temporary file that's somehow created from a bitbake class file that somehow is created by (I assume) the setup.sh script.
The file is that the temporary file is created from is: edison-src/poky/meta/classes/kernel.bbclass, which is not in one of the directories in the original tarball.
Now I need to figure out how that file is created. This is a VERY convoluted build system! It's no wonder it only works on a very limited set of distributions.