I was trying to work around an issue, but now I see my issue is independent of 32-bit or 64-bit systems.
I'm running Windows 7 Enterprise SP1 64-bit with Internet Explorer 9.0.2.
I have Secure Lockdown set for No navigation, Fixed bars/menus, No downloads, and No open dialog.
Going to http://www.highmarkbcbs.com, I see the button "Get Adobe Flash Player". Even though I have "No downloads" active, I can download and install the beta Flash Player for IE 64-bit. That can't be good.
(When I ran on a 32-bit Windows system, I didn't see the button because Flash Player was already installed. When I uninstalled it, I find I can still do a download from labs.adobe.com dispite the Secure Lockdown setting.)