Significant, as here, and not odd, mysterious or conspiratorial. That is, I would take it as confirmation of an established and meaningful relationship that is presumably constructive.
“If a Cardinal, Bishop or prominent Catholic layperson said the exact same thing to Rep. Paul Ryan, would you find it odd, mysterious, significant or conspiratorial?”
The Catholics, for all their problems, aren’t a massive secretive religious cult that is anti-Christian, extraordinarily controlling, engages in brainwashing, and systematically deceives its followers and the world about its own teachings and history. Well, unless you believe the Dan Brown books and think that the Catholics have a division of Albino Monks trained to kill uppity, smug liberals who imagine things in the Mona Lisa and Last Supper paintings.