I think the problem was a combination of two issues.

First, the warning in 16.17.2.2 is a bit hidden. Kind of squeezed in 
between CDLL, etc and PyDLL. In contrast, 16.17.2.4 does a much better 
job, because it restates the fact that the GIL is released at each and 
every item. I think this is much better, because chances are high that 
you actually read the entry completely. In contrast, in case you 
are in a hurry you might miss the warning in 16.17.2.2

I think the second problem was that back then I was not aware of the 
fact that you need the GIL to call the Python/C API. That was a bit 
stupid indeed. But as a Python beginner it was just not obvious. Maybe 
the Introduction of the Python/C API needs some work, too. No GIL 
mentioned at https://docs.python.org/3/c-api/intro.html.
Furthermore, the examples at 
https://docs.python.org/3/extending/extending.html also do not talk 
about the GIL.