From our experience here, it doesn't matter if you're downgrading or installing OS X from scratch. Also, we had this issue with physical as well as (VMware Fusion 8.1.1 Pro) virtual machines with exactly the described symptoms. Upgrading seems to work OK.
The cause seems to be that copying the installation file downloaded from the Apple App Store (called
Install OS X Mavericks.app or
Install OS X Yosemite.app or
Install OS X El Capitan.app, couple of GB in size) to a non-Mac file system (Linux
ext4fs shared over Samba here) removes or alters some file meta data. That at least is our best guess about the actual cause.
The file is still good to create USB boot sticks (which later on then expose the same problem) or go through the basics of a VMware VM setup, but when it comes to the point of actually installing the OS, clicking the Install button does nothing and the error message detailed in the question is printed to the installation log.
Solution: Store the installation medium on OS X file systems only.
See also this VMware forum post for more information. As mentioned, the problem is not related to VMware though, it's yet another OS X issue.