I know that with the AMT credentials, one can read the AMT event log and figure out whether the system woke up because of AMT alarm clock. Is there any way to figure this out without having the credentials?
The short answer? No.
As you mentioned, you could check the event log but managing the credentials can be cumbersome. The 'expected' usage model (for lack of a better word) would be to run an agent on the system.
For example, if you want to perform a backup everyday at midnight you can use alarm clock to boot the system. Then the agent can determine that a backup has not been performed since yesterday. Are that point it will perform the backup operation, then power off the machine. If the machine is restarted (say the user pressed the power button) then the agent will not perform another backup until the next day.