OK, for anyone else out there who find this issue, here is the resolution:

1. If you install Quickbooks on a machine, all users need to have access to the installed version of Quickbooks, REGARDLESS of whether they will ever use QB. If you don't do this, it is possible you will run into this issue, for anyone who doesn't have access to the location where QB is installed. I consider this to be a failing of QB design, but it isn't going to change.

2. If you need to have QB setup this way, you can try DENYing access to this key to anyone who doesn't need access to QB:

Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Installer\Features\882996FDC8DC9B94B9627EA5816983B7

It looks like QB puts entries into the registry that requests Windows to check QB installation of modules every time you open certain Windows or application features, EVEN IF QB isn't being used by that user. Because it is trying to do something with Windows Installer with QB stuff, and the user doesn't have access to the files involved, you can't quit the installer.

Anyway, I'll try to keep this post updated if I find other keys that need to be excluded.

Thank you all.