When the narrator says, "neither refused the meeting" he means

This can mean two things. Depending on how it was used, (if both characters were apprehensive about being together), it could mean that neither wanted to have the meeting, but they were fine to go forward with it. OR If they both wanted to meet for a certain reason, and they both came to the same conclusion at the same time, then they were both fine to meet. Either way, the meeting was consensual.

they are both going to the meeting