Hmmm. It seems my tests are incorrect; on a normal, untouched 64-bit system (so: able to run 32-bit progs) I was neither able to run the 32-bit hello-world-program. It appeared I had to do this first:
sudo dpkg --add-architecture i386
sudo apt-get install libc6:i386 libncurses5:i386 libstdc++6:i386
… and after that the 32-bit program worked.
I will remove my other two comments.