Attempt to call AccountUpdateEx_API even under admin user results in the error
System Error No access rights granted to method
The issue is caused by the bug with id #PBA-67497 ("AccountUpdateEx_API is not assigned to any privilege").
Until the bug is fixed, apply the workaround:
Add the line to file /usr/local/bm/conf/BM.methods.list
BM Account AccountUpdateEx_API ACCOUNTS_CREATE_MODIFY
Note that until the bug is fixed, the worakound is to be reapplied with each BA update installation.