Guys, I finally solved it and happy to say it has nothing to do with authorizations. Of Course, the fact I could only observe this behaviour with a non-ADMIN user lead me in a wrong direction.
I assume, I ran into kind of a timing issue where a dependent DBRA formula was evaluated before the referred element's
ng-model was ready. I think that for ADMIN users, the timing was not an issue, but probably some additional steps are performed for non-ADMIN users to check security etc etc, so that it takes a little longer.
The situation was that I retrieved an attribute value, stored it in a ng-model, and used this model to feed the tm1-element of another DBRA, which then did not get the result as obviously at the time of evaluation the ng-model was not yet populated.
Taking out my Statement from the active form and having it in the header first seem to make things working, but at the end only changed the timing a little bit, so this was also misleading.
At the end, I could not manage to force the right evaluation order of these two dependent DBRA. I now put a hidden SUBNM in between and feed its tm1-default-element with the first DBRA, and the second DBRA looks up the SUBNM's ng-model now rather than the first DBRA's ng-model directly. That way, Angular seems to do things in the right sequence.
Sorry for bothering you with that. I hope, someone running will make use of this post if running into a similar situation.