I am now certain that ADOBE SUPPORT is comprised of idiots.
Here was their response to my message on FACEBOOK:
We just received an update from our LR team that says the Application Manager has been updated in a recent build of the 4.3 update. If you are still experiencing issues, LR can be updated by going to the Help menu in Lightroom and choosing "Check for Updates". I hope this helps! Thanks, Madison
Here, in turn, was my response to them:
You folks just don't understand the issue huh? You have done absolutely nothing to help me. Let me clarify the issue one more time:
The app manager shows that I have 4.3 installed, when I really have 4.1 installed.
When I go to "Check for Updates", Lightroom directs me to physically download the LR 4.3 software. When I try to install that LR 4.3 update, it is unconnected to Adobe Creative Cloud -- so it attempts to install itself as a separate Lightroom Application --- separate from Lightroom 4.1 -- it then asks me for a registration/serial number -- SERIAL NUMBERS/REGISTRATION CODES ARE NOT INCLUDED IN THE ADOBE CREATIVE CLOUD MEMBERSHIP.
So, in effect - what you just told me to do was exactly WHAT I TOLD YOU DIDN'T WORK IN MY FIRST MESSAGE.
THERE IS A PROBLEM WITH YOUR SOFTWARE.
JIM - thanks, uninstalling LR 4.1 worked!
Worst part is that no one at Adobe seems to understand that there is an issue with their software.