Symptoms
Executing OrderFinDetailsListGetExt_API under the user credentials fails:
<string>U3lzdGVtIEVycm9yTm8gYWNjZXNzIHJpZ2h0cyBncmFudGVkIHRvIG1ldGhvZApFcnJvciBDb2RlOiAweGIzOTBiZWM1LgpSZXBvcnQgSUQ6IDkK</string>
which is base-64-encoded message:
System Error No access rights granted to method
An error is reproduced with any user, even those that have full administrative rights (e.g. admin).
Cause
The issue is caused by the bug PBA-60910 ("API method OrderFinDetailsListGetExt_API fails when being executed under user credentials").
Resolution
Update to BA 6.0.4 or above where the bug is fixed.