I resolved this by running the Updater, which is unexpected because I assumed downloading the current addon manager installer would do the same as the updater. Wrong in this case.
Yes, installing the Addon Manager will run the FSDT Live Update (you surely must have noticed it did), exactly as if you would run the update manually. Its starting the same, identical, updater.
So no, it's not normally possible that installing the Addon Manager would give you a different result than running the updater. However, we have learned that 3rd party software, usually the antivirus or a firewall, can make the impossible to happen.
For example, and antivirus/firewall might have blocked the updater when it was started by the Addon Manager, mistakenly flagging it as a dangerous operation, but might have allowed it, when it was started by you personally.
That's the only possible explanation, since the updater is clearly the same program (the Couatl_Updater.exe in the Addon Manager folder) so, it shouldn't give different results unless, of course, something else is interfering.