I've just tried to change the password of the user SYSTEM and I didn't run into a privilege issue.
Naturally you need to use a User that is Member of the ADMIN Group in order to be able to change the SYSTEM password.
Having said this, It didn't behave quite the way I'd like to, so I'll have to fix that.
If I use the user SYSTEM to change its own password, it does it wrong and I had to restart the server after the password change.
This of course shouldn't be necessary.
I've already spotted the flawed part of the code, but I'll need some time to fix (and for all test) it.
Currently I'm out of office, but I'm confident I'll be able to repair this soon.
Sorry for the hassle.