After communication with Esri Support in Redlands, they created a new documentation bug
#NIM085420 ArcGIS Server Administrator API for 10.1 help document states that there is an operation to change the password for a user account but none exists.
As for a workaround, the one that Ismael suggested above is how it can be done for builtin user stores. For other types of user stores, just directly make your code work the user stores' API.