Never mind. I found the answer myself whilst waiting for the post to be moderated.

After adding my user to the boinc group, it's essential to start a new shell before starting boincmgr.

Incomplete docs, not very helpful error messages and lack of logging are my favourites. :(

A somewhat better installation guide can be found at http://boinc.berkeley.edu/wiki/Installing_BOINC_on_Fedora. They speak of Fedora 17 when Fedora 24 is nearing at this moment, so it's a wee bit outdated ...

It suggests that you add your username to the group boinc if you want to edit some administrative boinc files easily from your regular user account. That should not be necessary. Neither is it necessary to 'chmod g+rw' anything in /var/lib/boinc, nor is it necessary to link gui_rpc_auth.cfg to your home directory if you install BOINC from the repositories on a more recent Fedora OS.

When everything is running fine, you should see this (mind columns UID and CMD) after issuing the following command:

$ ps -fu boinc
UID        PID  PPID  C STIME TTY          TIME CMD
boinc    12920     1  0 Feb12 ?        00:00:00 /bin/bash /usr/bin/boinc --dir /var/lib/boinc
boinc    12921 12920  0 Feb12 ?        18:38:33 /usr/bin/boinc_client --allow_multiple_clients --dir /var/lib/boinc
boinc    24143 12921 88 11:51 ?        00:37:16 ../../projects/www.worldcommunitygrid.org/<snip>