What you see in the Control Panel is the "Global Settings Manager" which can and does remain even if the Flash Player isn't working or is partially removed. Where you need to look for the Flash Player is C/Windows/System32/Macromed/Flash and C/Windows/SysWOW64/Macromed/Flash (on 64 bit systems).
Unfortunately I don't deal with MSI or network installs, but I'll pass this along to another member who has experience with them, and get you a good working link for both installers.
Thank you both for your responses. All the affected machines are 32-bit. I see both ActiveX and plugin versions installed in the control panels.
The date on the 126.96.36.199 MSI digital signature are as follows:
plugin - Monday, January 06, 2014 10:02:50 PM
activex - Friday, December 13, 2013 6:09:54 PM
Here is what I see in C:\Windows\System32\Macromed\Flash\: