This seems a difficult situation, at least for me, because I can understand both sides of the equation.
It seems it's fear driven from both sides.
The mono person doesn't want to do anything that might threaten her self image and identity (mono). Must be really important for some reason ? Being forced to meet the other love really drives home the fact that she is NOT in fact involved in a mono relationship except in her own mind.
On the other hand, the poly GF likely needs to have a certain sense of security about who she is indirectly involved with and feel good about that. Because meet or not - they ARE involved ! Can't change that fact. And your warning flags naturally go up when someone doesn't want to meet/acknowledge your existence. What are they hiding ? How could that affect me ? Etc. Natural and wise in most cases.
I guess the only win/win I could see coming from this would rely on the hinge. The poly GF would have to have such deep trust in her SO that she could get comfortable with a total unknown being in the picture. The hinge would have to believe that in at least this case, it's acceptable to nurture someone's else's fears of facing reality and that that behavior won't have any further implications down the line. That's a big leap to me. At least my experience has been that people who insist in burying their head in the sand end up with a mouthful and often smothering to death. Not a pleasant experience for the lover standing (or kneeling) beside them to live through. If you get my drift.
Not a good situation it seems.