User is not allowed to run test panel under Ni-Daq's "Measurement and Automation" (the choice is grayed out). A program that uses Ni-Daq's libraries terminates silently with user credentials. Both problems are related.
Solution: Users who want to be able to run the above mentioned programs must be given Modify or Full control permissions on this folder:
C:\Program Files\National Instruments\Shared\platform\memory\sharedMemoryFiles
It took a lot of research and experimenting with permissions on files and registry keys to reach this conclusion, but it seems consistent that this was the problem.
Caveat: When connecting to the server via Remote Desktop as a user, I was not allowed to run the test panel or other programs using the Ni-Daqs libraries, even if the above solution was applied. Being an administrator, I was allowed. Researching the problem via Remote Desktop at first certainly put a few extra hours of work into finding the solution :(
Caveat 2: On older NT4 systems this will probably not be a problem, because it does not restrict the permissions on C:\program files to readonly for standard users (by default).
Caveat 3: On older Ni-Daq versions (ver. 6.9.1 comfirmed), the above mentioned folder does not exist. Whether that means that the problem is then irrelevant or to be solved differently is not known.