Here is a small hint that I hope might be useful to other poor saps that experienced the same issue as I did.
My Setup:
Host: Windows 7 Enterprise - build 7601 SP 1
VM: VMware® Workstation 12 Player 12.1.1 build-3770994 (free)
Guest: Fedora release 23
I naively failed to install open-vm-tools-desktop. I say naively because I had no idea such a thing existed, nor do I understand why instructions to install open-vm-tools do not (or at least where I read them, do not) include mentions of this package.
Installing open-vm-tools on its own appears to be nearly useless - the desktop package makes the copy and paste function - probably the single most important function of VMTools - work.
So, there you go. Install open-vm-tools-desktop, and copy-paste should work
