After trying once again, VDR managed to tune to added DVB-T channels and find other channels from same multiplex. Soon afterwards it stopped responding, wrote lots of "ERROR: 663 ring buffer overflows (124644 bytes dropped)" to "/var/log/syslog" and consumed lots of CPU time. "killall -KILL vdr" solved that problem and VDR got restarted. This time both tuners worked properly for streaming and direct watching/listening.
Since "I did not touch anything" and things suddenly started working, I wonder if they still work on tomorrow or after next reboot.