The documentation should be taken literally, i.e. your second interpretation no answers which have a positive vote is correct! This is in line with how the UnansweredUnanswered tab is handled, see Why does the “Unanswered Questions” tab show questions that have answers?
I'm trying to get questions with 0 answers using the API.
You could start off from the /questions/unanswered
route, from its result set you'll 'simply' need to filter out all those answers where the answer_count
field is 0.
How 'simple' the latter really is depends on the client stack in use of course, i.e. you might be able to include the filter criteria in your request already, but otherwise you should always be able to search through the raw result array.