Chris,
Thanks for the link to the MSDN article. In the meantime, I've unraveled one more small piece of the puzzle: The reason that this works on a VM is that the VM Tools are installing something that resolves the issue. Here is how I determined this:
1) Install a clean copy of Windows 10, Version 1511 on VMware Workstation Pro 12.1.0. Do NOT instrall the VMware Tools! To do this, make sure you go through a manual install of Windows 10 because if you allow the VMware Easy Install to perform the installtion then it will install the VMware tools. Make the Network adapter a Host Only adapter so that I can connect to the physical machine on which VMware is running and copy Symantec System Recovery to the VM.
2) Try to install SSR. It fails, just as it does on the physical machines.
3) Now install the VMware tools.
4) Try to install SSR and it will now succeed.
So at least now we know that the issue can be reproduced on a clean install on a VM as well, you just have to prevent the VMware tools from installing.