Both the gap in solutions and the assumption of outcomes undermine this argument.
It hinges on the assumption that the Vatican or its metaphysical emanation, the Holy See, is a state.
This assumption, by and large, was a fair one, justified by our particular experience.
c.1300, "the reception, uncorrupted, of the Virgin Mary into Heaven," also the Church festival (Aug. 15) commemorating this, Feast of the Assumption, from Old French assumpcion and directly from Latin assumptionem (nominative assumptio) "a taking, receiving," noun of action from past participle stem of assumere (see assume). Meaning "minor premise of a syllogism" is late 14c. Meaning "appropriation of a right or possession" is mid-15c. Meaning "action of taking for oneself" is recorded from 1580s; that of "something taken for granted" is from 1620s.