No, this is THE logic. Vatican didn’t want to get involved (can’t blame them, if somebody tried to drag me into that mess I’d wonder why they hate me so much) but didn’t want to say “we want nothing to do with this”, so they said “we’ll work through the UN”, knowing full well they aren’t in the UN. Now their hands are washed and they’re not involved.
You are trying too hard to avoid the truth.
It is ignorance to try and deny supporting the UN to manage a process is somehow not supporting the UN’s political and ideological desires just because you are not an official voting member.
Leadership demonstrates their purpose by that which they align with. The Vatican aligned with the UN in this. The Vatican knows full well anyone they state as being preferred as the implied support, that is hgow politics works.
The clear answer if not engaging would have been to not accept and then NOT state who you think should do it. The Vatican instead decided to become active in the conversation when they stated the UN as a preference.