Kari, you are my hero for mentioning the Task Scheduler.
I decided to investigate that and I found an entry that my back up program created (see image)
Conclusion: The Task Scheduler CAN and WILL wake the computer up!
(I am very curious to how it actually manages to do that!!!
(Also noticed it started 6 seconds BEFORE the actual time... the description of one of
"policy change" events mentioned something about adjusting clock...
Thanks again all of you for your help!